MDF is most useful on the river. There are no cards to come and no more equity to realized. The more useful way to look at it is the fold equity part, or 1 - MDF.

In your examples, the 3 bettor is risking 10bb to win your bet (3bb) plus the blinds (1.5). So, he is risking 10 to win 4.5 or 10/10+4.5 which = .69. If you subtract that number from 1, you get 31% (same as above). If you follow the same procedure for the 8bb 3b, you see that he is risking 8 to win 3+1.5 or 8/8+4.5 or .64. If you subtract that number from 1, you get 34% (same as above).

I personally find the "fold equity needed" part more useful than the MDF part of the equation. If you look at solvers, in most instances, the numbers are pretty close to MDF (meaning, solver defends close to the formulas, but there are outliers).

When facing bets, I like to ask myself "how much is he risking and how often does it have to work?". In you above examples, if he 3 bets you to 8bb and you fold more than 64% of the time, they would refer to that as printing %. Same as your 1/3 pot flop bet example, they found that people over fold to the smaller bets and thus many people adopted the strategy.

More important than the above is to construct your continuing and your folding range based on the size presented. Smaller bets you need to continue more often and the bigger the bets get the less often you have to continue.

In general, I would say it is more important to focus on the pot odds in game and also look at the bets from your opponents from their perspective (the fold equity part or his risk/reward) up until you get to the river.

MDF is really really overrated as you said, since it does not even consider ranges equity. Again on the flop example as well, it is completely dependent on the board and there are some boards where you are completely fucked. If you try to defend these boards solely based on mdf then you will be adding hands into your preflop ranges that are -ev and it will screw up your entire game.

The other problem with this calculation is that it ignores the other players to act. SB/BB will do some of the defending for you.