Survivors classes in the extremely unlikely scenario of P = PSPACE If its proven today that $P=PSPACE$ the whole polynomial hierarchy collapses. Moreover since $BQP \subseteq PSPACE$, it will also result in $P=BQP$.

However unlikely the above scenario is, hypothetically if this were the case what are the complexity classes (the most important ones) that will survive this collapse into $P$. The classes we are talking about:


Should be above $P$ (thus $L, NC, NL$ etc. could be temporarily ignored)
Are interesting and open enough to be studied (thus $E, EE, ALL$ etc. can be ignored)


We are concerned about both the traditional as well as Quantum Complexity classes.
The time hierarchy theorem still tells us that
$$\mathrm{P}\subsetneq \mathrm{EXP}\subsetneq\mathrm{2\text{-}EXP} \subsetneq \dots\,,$$
and likewise for the analogous space classes and nondeterministic time and space classes.