It is a level-based game, there are just classes you could play that have worse than low BAB and poor saves.
d20 Call of Cthulhu is a level-based game. It has level progression tables for character advancement.
Mutants & Masterminds is not a level-based game.
If you wish to challenge either of these, I will require evidence. (Note that you cannot prove a negative, therefore no proof has been provided. You can prove a positive, therefore proof is required.)
Because I don't believe that absolutely everything should be bought with points, In M&M every single save must be bought. I just don't like that option. I prefer to spend my points on powers, skills, feats, and attributes. And even feats is iffy for me personally, but still doable.
M&M agrees with you. Only things that will have game-mechanic effect require points.
A place to live (not a super-base, just a home with a bed) does not require points, for example. Having a cool costume doesn't require points. Having a particular appearance, accent, mannerism, and so forth, don't require points unless they are supposed to also have a game mechanic effect.
Your character's ability to affect foes and resist their effects does require power points, since it is purely controlled by game mechanics.
You,
Quantum, apparently don't like purchasing saving throws. The implication is that you want them to be assigned to you by the game, using a "table" and a declared choice of "defensive" or "offensive". How they would scale is in no way covered (M&M doesn't have levels, so the CoC method won't work), so there's a big whole in your proposal.
The reasons for your feelings are unclear and obscure to those of us following the thread.
Still, take a look at the Mastermind's Manual, chapter 1, pages 18 and 19. That might work for you.