Oh I'm sure they record in higher resolution and bit depth. But as far as 16/44.1 goes, there's no difference between CD and FLAC.
Quick crash course. There are two factors affecting the quality of the digital file:
Sampling rate (44.1kHz): How many digital samples are taken each second. The more samples you take, the higher possible frequency you can record without errors. 44.1kHz theoretically is more than enough to reproduce human range of hearing (< 20ish kHz).
Bit Depth (16 bit): Affects three things. Resolution - How accurate each sample is. There will always be some rounding error when you convert an analog level into a digital one. The more bits you have each sample, the closer you are to the true analog level. Signal to Noise Ratio - How much noise (due to rounding errors) is present in the signal. Dynamic Range - The difference in volume between the quietest possible sound, and the loudest possible sound.
So you can see, we can technically benefit from increased bit depth, but 16 bit is already very good. 24 bit pushes the limit of the DACs and ADCs we use. Increasing the sampling rate theoretically will not provide an audible difference, but it can be useful for other reasons.
Studios do record in higher resolution files like 24/192. We don't get these files though, because 16/44.1 is the standard for CD's. 16/44.1 is already very good and lossless files are already big enough. Once you increase either of the two factors the file size increases very quickly. Heck, we can't even get lossless 16/44.1 downloads because enough people are happy with MP3s that it is not cost effective for companies to give us lossless files. There's simply not enough motivation for companies to provide us with better files.