This reminds me of the concept of "no zero days": To build up a habit or a skill, do at least the minimum required to acquire that habit or skill. If it's push-ups, do just one push-up, just to keep the streak of no zero days. If it's writing code, write one line of code. The magic is that, the greatest friction comes from the resistance to doing anything at all instead of doing it all the way.
Exercise does however explicitly require some zero days, a lesson I've learned the hard way. You need time to recover, and that involves doing nothing.
To my experience this is only true if you totally max yourself out when exercising. An alternative is to do light (ish) exercise every day. Makes getting totally ripped pretty much impossible, but it makes staying fit easy, because it's easy to build a habit around and it's easy to make fun.
A streak strikes me as a very different thing than a habit. Habits aren't hard to pick up after a break, streaks are. I have a hard time to figure out what it means for someone to "purposefully break a habit", except in the context of bad habits of course (eg a smoker trying to not smoke for a day). This is my whole point I guess, if you manage to make exercise a habit and not a streak (by making it fun, and feeling good, and having space for it in the daily calendar), then you can stop worrying about 0 days altogether and just do it every day except when you don't.
> by making it fun, and feeling good, and having space for it in the daily calendar
That's definitely the healthiest approach to it. I agree with you it won't matter if you stop for a while or not, as it was done for pleasure in the first place.
The OP comment was pretty specific and explicit that it is not going hard every day, it is about doing some minimal something every day to maintain and reenforce the habit. You asserted that you “explicitly require some zero days” but that is not true. You can have no zero gym days by using your heavy lifting rest days to do mobility exercises and stretching.
If you're damaging the muscle while stretching… Okay, I'm gonna assume you're not letting any of you're stretches produce pain. You should feel tension, only, which should not be harmful.
In my experience and training, stretching every day is practical and effective. Skipping a day can cause noticeable tightening. Tension for the purpose of becoming more limber should be held for a minimum of 10 sec, but 30 sec. is a much better basic level. There should not be tremor or pain; either of those will be counter-productive and potentially result in injury.
What are you basing that on? Elite mobility coaches like Kelly Starter recommend daily - even hourly -mobility and stretching workouts, with the goal of being constantly mobile.
With many types of skills putting in some time every day can be very beneficial.
Keep in mind though that with things like strength your body also needs recovery time (in fact your gains happen during recovery, not during the workout).