Consistency v restrictions and boundaries

One way is that they may be used as inputs for other systems

Nice sticky bowl model

Great Darwin quote.

Very interesting with thanks

i) Maths is inherent to nature, so for example we can show retrospectively that maths applied before the human species evolved and before maths was discovered.
ii) Physical problems that can be expressed as maths problems can be analysed and potentially solved as applied maths problems.
iii) Some physics problems may not be expressible as defined or definable maths problems. This follows inter alia from completeness and computability theories.
iii) Potential maths can exist without physics, but actual maths is constrained by the physics of information processing, so one might argues that in this respect maths and physics are mutually-supporting.

Stable vacuum might be more comfortable.

Sounds highly plausible, but so at this point did inflation. The bottleneck bounce looks like the point where the theory might most easily go wrong.