But that's sort of built into the game, isn't it?

No, I don't think it is, and the reason why is because nothing in the gameplay necessitates random purchases. That isn't part of the game. In fact, several CCGs have gone from a blind-buy model to a fixed-distribution model and the gameplay has not changed at all. They did this with Netrunner, Call of Cthulhu, and some others. Fantasy Flight has a whole line of these called "Living Card Games".

It's easy to imagine Magic being sold in a similar way: instead of randomized boosters, you buy boxes of cards that contain 4 of each card, you build your decks, and off you go.

At the highest levels of play, money isn't a factor. The players who win Magic tournaments aren't the ones with the most money. If that were true, it would obviously be a broken game, and nobody would be playing it anymore. Instead, wealth is a gatekeeper. You have to have a certain amount of expendable wealth to be able to play at the highest levels. If you made all of the cards equally accessible, it would change nothing except lowering the bar to entry.