Our senses can easily trick us, especially hearing. I have seen respected reviewers failing blind tests. In high-end audio you often have to really focus on the differences which you simply wouldn't notice if you were just enjoying your music. These differences can often be measured in $£€ hundreds or even thousands.
At the same time the sensitivity of our hearing differs too. Some can easily hear the subtle differences where it is all the same for others, even in 'audiophile' circles.
You have to put a personal price tag on what difference (improvement) is worth it for you.
DAC burn in or cable burn in I don't really believe in. Yes, DACs and cables can make a difference, but they don't really need to 'burn in'. It is more like your brain/ears are adjusting to the new sound. Some people can adjust quicker, some slower. Even folks who can easily and quickly distinguish between two new sound profiles it can take 2-3 days for them to
fully adjust to a new sound or fully appreciate it.
Also there are headphones/amps where the brain adjustment happens quicker/easier and sometimes it takes more time to appreciate something. For example the Nighthawk takes days to fully adjust to while avoiding listening to anything else. When I am coming back to my home system after 2 weeks holiday it always takes a day to really appreciate it again. Of course it sounds great immediately, but takes time to see (or rather hear) why I spent so much. Of course, the following day I fall in love again.
I can btw recommend this antidote for upgraditis. Stay away from your system for two weeks and see if you really want to purchase that next headphone or amp. (Also reading positive reviews of your current setup can help.
) Of course, I know it is just delaying the inevitable. Or maybe not if you have done these rounds for hundred times...
Some headphone drivers ease up in the first 100 hours of usage due to mechanical movement. Mostly the treble becomes smoother and the bass fuller. Some amps can also sound a bit thin or raw in the beginning and they become more lifelike or fuller sounding. DACs? That is brain adjustment in my opinion. Even with headphone burn-in more happens in the brain than in the actual drivers. There is some degree of burn-in with certain equipment but it is ridiculously overemphasised in this community.