You can fake stuff like this, but it will be fake.
There's a hard division between "simulation" and "animation." Simulations are history dependent -- they may be deterministic but the state at any given time is dependent on the state of the previous frame. Animation is arbitrary, so there's no necessary connection between successive keyframes (although there are some mechanisms, like expressions, which will allow you to set a value now based on the value of something else at a different time).
If the effect you want does not need history, you can definitely make that work; for things like interpenetration fixes that will work fine as long as they are entirely derivable from a current-time position. If you can describe the effect entirely as a function of positions then it's totally doable.
You'll definitely find that the instantaneous effects add something, but you'll also find that many things resist that treatment in subtle ways. The soft body example. again, shows the limitations: you can definitely convert interpenetration into deformation. for example, but things like the wobble that results from a soft body interaction dissipating energy over time won't work and may appear to be visibly missing. Lag and followthrough are often very visible artifacts, and those are a lot harder to get by without.
TLDR - works for limited cases, but it's not possible to completely replace simulation with functional deformations.