Why are so many wave functions associated with hydrogen?
1.Would an unperturbed electron ever go outside the lowest orbital?


First, there is no such thing as "outside the lowest orbital" because the lowest orbital has probability density at all points in space (no nodes).  

But yes, at a given temperature electrons will be distributed amoung the energy levels in accordance with a Boltzmann distribution.  


  2.At some point the perturbation (excitation) energy would exceed the ionization energy, so above that certain energy, no orbitals could ever be populated, so what's the point of having all these solutions?


There are infinite solutions none of which exceed the ionization energy (the ionization energy is only approached as n approaches infinity).

Think of a series like 0, 3/4, 8/9, 15/16, etc. where there are infinite members without reaching 1 (1 is approached in the limit of infinity).