Training: is regularity important?

I would be curious to hear more expert athletes/coaches insight on how important it is to train following a regular schedule.

This is what I mean: let us say that in a week we have a certain total volume of training - in my case that is, at least, MS, FS, 3 split sessions of F1 and one session of H1. Does it matter, and why, if I consistently train the same exercises in the same days, rather than still doing them all but on days and combinations which vary from week to week?
Let me repeat that the idea is that with both "formats" I am doing the same total amount of work.

I am not a big fun of tight organisation, and I find the approach of adjusting the sessions week by week appealing.
However, I have started thinking that a fixed schedule would be more beneficial. My reasons:

- Knowing in advance which days you will be training allows to program other things around it. In a sense, it could end up allowing more freedom, without the struggle to make room for training sessions which have not been scheduled in advance.

- It is probably easier to understand how your body reacts and recovers from different workouts if the format and timing of the workouts are kept consistent.

What's other people insight on this?

Advanced schedule with waving intensity and volume through the week it is actually the best solution but it is still a fixed program through the week.

Holding some fixed parameters gives an accurate idea of how much work can be done and it works best with the linear programming. the linear programming has some limits but in the context of bodyweight it is the best solution since you do not know at what % or 1RM you are training. Also beginner do not need advanced programming with waving structure, this is something more suitable for more experienced people.

Keeping constant at least the number of sessions for at least 12 weeks allows you to understand if the frequency it is good enough to train and recover. altering the frequency at your level could have opposite results than desired. I have basically a fixed schedule since 6-7 years, it allows me to recover properly in between session. it is enough to move one exercise to another session that i will feel it in the next day.