Almost every type of drain cleaner specifies that they should NOT be
used in a toilet. Why is that?

Is it because they feel there is too much standing water in the toilet
due to the size of the trap?

Or does the cleaner have an adverse effect on the wax seal used for the
toilet bowl?

The reason I ask is I had a poorly flushing toilet and plunging it did
not improve the situation. I tried a snake but the trap of the toilet
and the direction of the drain pipe underneath it made the snake
ineffective. I ended up removing the toilet and used a snake. What I
discovered is the toilet met up with the tub drain pipe, and I know this
from the hair I pulled from the piping with the snake and the direction
the piping went.

The toilet flushes, but my guess is there is still some hair from the
tub that is restricting the flow. So my question is: If I were to
remove the water in the toilet and put some drain cleaner into the
toilet after the trap, would that cause any unforeseen problems?

I have already put some cleaner into the tub drain, and a snake will not
go into this drain due to the drain hardware of the tub. Thanks.