The "issue" can be test with just math that I don't master, more or less, and in part the answer to it depends on how you define "a bad starting hand".
For the sake of argument, let's say you have 60 cards in deck and draw 2 at a time, with a first draw of 7. Let's also assume that you are a shitty player and that 50% of your deck is made up of really expensive cards, and that 50% is made up of cheap ones (here = good starting hand) that are ready to be played in the early game.
However you do this, you have at least 50% chance to draw a good starting card every time you draw the first seven cards, in the sense that you can at the very least afford it. This is not even entirely true, because probability grows the more unlucky you are - if you drew 3 expensive cards then chanses are higher that you on the fourth draw will get a cheap one.
Yes, you might get a 7 cheap cards that you can afford on turn one, but they may be useless for some other reason at that point in time in the game. So, either you mulligan to get other cards, or, if whatever you get is a bad start, then your deck is broken and you should not win to begin with.
Despite that I'm not sure I follow you Nico:
You want to solve a problem by removing mulligan. The problem is described as people trying to get an optimal hand for the deck, and you imply that if a person has built a deck around 1 or maybe 2 cards, and that person really needs those 1-2 cards superfast, maybe even on turn 1, then that person shouldn't ever be helped into victory by doing a mulligan since the mulligan gives that person a greater probability of succeeding with his bad deck. Am i right? (If not, what other reasons are there for not wanting to allow the mulligan?)
The player has a chance of at least 1,6% of getting the card he needs on turn one, every time he picks one of the 7 first cards, and growing. Assuming he only has one single copy of the golden card ; ) If he has 4 copies he has 6,5% chance of getting the card, 7 times in a row, and growing, on the first draw. (Sorry I don't know the math to accumulate them and get the "real total chance...")
A mulligan wouldn't "double" the chances to get that card. It would double the opportunities, with the same chances. So, still pretty low chance even if you do include a mulligan, and even if it's 4 copies of the card in the deck.
In any case, I don't see a player that builds a deck around 1 or even 4 copies of one single card actually winning any tournaments or winning more than losing. If his while game depends on it he should lose at least 90% of all games, unless he plays other morons... in which case not the best, but "the least idiotic" deck, will win
Furthermore, if there are worries about card positioning in deck and fetching then a lot of other mechanics in the game would also need to be revised for the same reason: Re-shuffling, card fetching cards/abilities, random draws et.c.