Shaped maps and atlas progression

I am asking for clarity on how atlas works when it comes to shaped maps. In essence I finished all but Perandus map, but I got thinking if the shaped maps wasted my time in a quick progression.

I'm not exactly sure how to phrase this so please help me understand.

Do the shaped maps increase the pool of possible map dropped of that tier? So less shaped t10 maps would increase the probability of t10 map dropping that I actually need (connected to an area I haven't unlocked)?

Would you progress faster if you waited to clear all maps of the shapers orb (and 1 level above it) before using the shapers orb?

I find myself having a difficult time explaining this.

Correct. Furthermore there may be certain merit in farming maps from all corners before opening a new tier. That way you can direct your farming efforts by choosing which maps to run. However if your pool of a particular map is exhausted you'll need to spend time getting more of that map.