Except that it's not.
If you and I played a round of golf, where I used a standard set of golf clubs (not cheap) and you used a hand-whittled tree branch, it's highly likely that I would beat you regardless of our relative skill level. This does not mean golf is "pay-to-win", though; if you and I both played with the standard clubs, skill would determine the outcome. And even if you played with an average but acceptable set of clubs while I splurged on super-fancy clubs, you'd still beat me reliably if you were the more skilled player.
Magic is much the same way. There is certainly a financial barrier to entry, which must be cleared if you want to succeed in competitive play. And if you pit someone who has cleared that barrier against someone who has not, skill is much reduced as a factor in determining the outcome. But competitive Magic is like everyone having at least a basic decent set of golf clubs: everyone playing competitively has made the up-front investment in the game, and now they are distinguished by skill rather than further spending.
After selling my collection of cards, I find that I can still enjoy playing the game using the "draft" format: invest $9 or so for three packs, then have a pleasant evening of play. No more expensive than seeing a movie, and the playing field is more or less level.
EDH started as a community driven format with no official support. The community decided that your deck must be exactly 100 cards with no duplicates except basic land. This slows the came down and forces more board interaction.
On top of that 1 of your hundred cards must be a Legendary creature. Everything in your deck can be of a color from that creature and you will always have access to that creature throughout the game. This constrains deck construction and makes it really hard to splash a color for one $50 that would be perfect. Always having access to commander is a comfort to new players and opens new strategies to veterans.
To further combat this I have a pool of 30 or decks that I build with my friends and we play mostly from this pool. No paying to win if we are paying together.
I have a tourney-competitive EDH deck that, according to current prices, costs about $400. That's a good bit... but replacing 4 cards with cheaper counterparts brings it down to $63. And I have recently seen at 2 other good EDH decks under $40 from someone who decided he wasn't going to spend more than $50 on any deck.
Definitely doable.
For more info on that, including what percentage each archetype makes up of the total Commander metagame and what each costs: https://www.mtggoldfish.com/metagame/commander/full#paper
I spent about £25 on cards, and was probably given another £25 or so by a wealthy friend. The game was fine when played against others who had a similar investment, but the group stopped playing because of eBay: our friends with real money could buy what they wanted, and the rest of us could never beat them.
I think it was the first thing we did which showed who had money and who hadn't. We could take cheap plastic Warhammer figures, paint stars on them, and declare them to be powerful wizard-mages. Computer games were easily copied, it didn't matter who owned a board game. M:tG ruined the equality...
I looked into the game again about a year ago, but there were so many new rules (new abilities, new card types) -- I decided I didn't want to spend that much time on one game.
I think I'll be sticking with the eternal formats where cards don't lose 90% of their value in 2 years.
The strategy and game-play dynamics were awesome. Not so awesome: the fact that the amount of money a player spends acquiring rarer cards and assembling a deck dictates their success. It's a pay-to-win game and I fucking hate games like that. Not unlike paintball, he who spends the most on gear wins.