What is the point of a class based system if it doesn't really matter what class you are, you can just do anything?
You can't. Why are you assuming someone can? Why do you keep injecting a foolishly hyper-permissive DM into this?
Class still matters. Class provides
guaranteed competence. There is no, or at least minimal, need for negotiation or justification; that's what class features
do, they clearly define how they work without needing to haggle or risk or eat costs. Having momentary, one-off events of special note does not erase the consistent, reliable benefits provided by classes. If anything, it highlights how special it is to
have those benefits: the Fighter can Action Surge several times a day with no harm whatsoever, while a Wizard risks her very life and livelihood even
attempting it.
If we followed your philosophy, we'd never have gotten any other classes but Fighting-Man and Magic-User. Cleric and Thief specifically evolved out of players asking to do improvised things. And if you prefer a more diegetic explanation: How do you think the first Wizards learned their spells? There had to be a first person to attempt to do something
without formal training.
We clearly disagree, and strongly, on this. I not only see it as an exploit, I am honestly having trouble fathoming why you can't see that it is one.
Gods providing divine aid is a classic trope; people turning in desperation to things they normally would not is a great story; the point of the rules of D&D (or any TTRPG) is to experience something interesting, while making difficult choices and leveraging resources available to you. An "exploit" is something which breaks the fundamental premises of a given game, leveraging the text of the rules against the spirit of play. Doing something
not written in the rules, because the DM is supporting improvisation, by definition cannot be "an exploit." You may think that it is
unwise to DM that way, that it trivializes challenges, but neither of those things is "an exploit." And, as I said, you keep assuming that this is opening up some horrific Pandora's box of infinite abuse, but you as DM always have the ability to not allow that to happen. If the players want to develop these abilities beyond one-off special events, they can invest in playing an appropriate class. Such (rare, special) moments of unusual behavior are in fact great justification for choosing to combine classes together: the Fighter taking a level of Cleric because they've found faith and been blessed, the Wizard taking a level of Fighter to toughen up because she wants to be stronger, the Sorcerer taking a level of Bard because he's realized he actually finds joy in raising others' spirits, etc.
Why would you consider allowing such a thing period, when there is a clear way to accomplish the goal in the context of the game already? Arbitrary costs imposed or not, you are absolutely giving clever players a massive amount of stuff to exploit.
Why? Because:
1. It builds toward interesting story. These are the moments that will stick with players for years after the fact. They are among the moments that define campaigns.
2. Risk, improvisation, and embracing complication should be encouraged. Slapping the player down with, "Welp, sucks to be you, guess you should've taken a level of Paladin or Cleric!" is at absolute best counterproductive.
3. Players, I find, are much more willing to consider new directions for their characters if they have a
visceral understanding of what they'd be getting. These moments offer that directly, and do so in a way designed to serve the story.
4. As I said earlier in the thread: Why do you play with players you don't trust? If DMs are supposed to be given such unreserved, universal trust instantly without any restrictions, why is it that players should be treated as horrific untrustworthy villains, rubbing their hands with twisted glee as they prepare to destroy all that their poor, beleaguered, hapless, put-upon DMs try to do with their
absolute power?