Hi Abtr,
This is my current understanding,
eager for correction, where appropriate...
Whether starting out balanced (with the secondary grounded from a center tap) or unbalanced (with the secondary grounded at the neutral wire), if you then float the secondary, you will still get the same amount of common-mode noise reduction as you had before floating the secondary, with the only difference being that if you started out balanced, with a grounded center tap, you will have just converted it to an unbalanced transformer with a floating Secondary.
So... In your experience, you have essentially said you prefer the sound of an ungrounded (floating) secondary to the sound of a balanced secondary (which, by definition, is grounded via the center-tap.)
I suspect the reason you prefer the floating secondary is because you've got a ground loop between one or more components that gets attenuated somewhat when you float the secondary that they are all sharing.
I'm not a big believer in balanced power, perhaps because I so strongly believe that the "magic" of common-mode noise reduction occurs via the Faraday shield that inhibits capacitive coupling from the Primary into the Secondary. In other words,
what work is left to be done, by the time the 60 Hz AC power has passed unharmed from the Primary through to the Secondary (via magnetic induction), stripped of any DC signals (Common-Mode noise) that have, at that point, already been attenuated 20,000,000:1 (-146 dB), in the case of the 0.0005 pF Topaz units? Whether we ground the secondary at a center tap (balanced) or ground it at the Neutral (unbalanced), the Common-Mode noise that came into the Primary on the Mains has already been diverted to ground by the Faraday shield(s), converting any residual common-mode into transverse-mode (normal- or differential-mode) noise - which most 1:1 transformers would just pass into your loads, but the Topaz Ultra-Isolators have some kind of double or triple Faraday shield configuration that manages to provide -65 dB of normal-mode noise reduction without using modern filter circuits (i.e. Y-Caps at the input, an X-Cap across the outputs (for modest voltage surges) or one or more serially arranged MOVs across the inputs or outputs (for heavy surge protection). Keep in mind that MOVs actually create some common-mode noise when suppressing normal-mode transients, and the Topaz can already absorb a lot of surge, at least until the voltages are high enough to saturate the transformer and penetrate the insulation of the windings.
OK, I got into a bit of a ramble, there, but to answer your first question... There are two reasons for putting only one component (one load) on a transformer with a floating secondary: 1) If you were to plug two components into one floating-secondary transformer, and the first component somehow shorted Hot to the case, you would be fine, until, by chance, at some point in the future, the other component shorted Neutral to its case -AND- you happened to touch both cases at the same time - allowing hot to flow into one hand over to the other hand. The probability of this happening is extremely low, but if the two components were plugged into the same transformer with a grounded secondary, you wouldn't have to worry about the improbable possibility. 2) Much more probable is the chance that you've got a DAC, CD Player, Blue-Ray player or other microprocessor-equipped component that's dumping digital "hash" common-mode noise back onto the power cord, where it could pollute the power going to any other component that's plugged into the same outlet, power strip, or transformer. You could also have one or more components that are equipped with SMPS, which are also known for dumping noise back onto the mains.
A well-made analog component, with a linear power supply, like an amplifier, is more likely to be a victim than a culprit, when sharing a power strip with other components, so these non-backwashing components can be plugged directly into a grounded-secondary transformer (whether balanced or unbalanced - your choice), but all the backwash suspects (DACs and other digital sources, plus anything with an SMPS) should be segregated from each other and from the analog components, by using floating-secondary transformers that themselves plugged into the one, larger capacity, grounded-secondary transformer. Each of the floating-secondary transformers will prevent any backwash noise from polluting other components - the common-mode noise attempting to flow upstream will be attenuated as it attempts to get from the secondary coil to the primary coil. (A transformer with Faraday shield can attenuate common-mode in both directions.)
It will also break ground loops - even if you have signal cables running between components - i.e. between a DAC and an amp - no loop can be formed to get back to a shared power ground when they are each plugged into independent, dedicated, floating-secondary transformers. Remember, each component with a three-prong plug still has a safety ground that goes all the way back to the wall outlet, through both transformers, per code, but neither the Hot nor the Neutral supplying power to each compoent is connected to that safety ground - at least not within their respective floating-secondary transformers. Joy!
You can, however suffer some leakage currents, caused by voltage differences coming out of their independent transformers - i.e. when an amp is plugged into the powerstrip of the big grounded-secondary transformer, but the DAC is plugged into a floating-secondary transformer that has been inserted between the DAC and the big transformer - the amp and the DAC will see different voltages, in which case, if you want to discourage leakage currents, you can really pull out all the stops and insert a high-bandwidth signal transformer, such as one of these, made by Jensen:
https://www.amazon.com/Jensen-CI-2RR-IsoMax-Isolator-Jensen/dp/B00ASVWYCS
or
https://www.amazon.com/Jensen-DM2-2XX-Iso-Max-Isolator-Jensen/dp/B00ASVWYO6
But to start with, I would encourage you to just ground the secondary of your main transformer (unbalanced is my preference), then insert Hammond 171 Series transformers (which range from 100 VA to 1000 VA and have floating secondaries) or a B&K Precision 1604A, ahead of each digital component or those with SMPS. Give that a try and see if it doesn't sound better than plugging everything into your single, floating-secondary transformer.
I would, however, caution you to use a Kil-A-Watt to measure the voltage going into each component when operating. Each transformer in a series will likely increase the voltage that came into it, even though they are technically 1:1, until you fully load them to their rated capacity - which you really don't want to do, especially for power amps, because you want to leave "headroom" for the transformer to supply instantaneous peak currents on demand, above rms current requirements.
If stacking two 1:1 transformers serially has your component seeing more than about 127V, you should consider getting an APC LE1200 voltage regulator, and setting it to an output voltage of 107V (the lowest of three available settings.) Plug your big grounded-secondary transformer into the voltage regulator, then the smaller floating-secondary transformer, and you'll measure something closer to 120V at the second transformer's output.