I don't understand how Arena can be a platform for competitive constructed Magic when you can't guarantee what cards you have access to. In the old client and in paper Magic, if you needed a card, you could get it directly from someone. That's not the case in Arena. You have to hope to open it (or a wildcard of the right rarity) from a pack. This limits competitive play to mostly people who have the time and luck to collect every card they need.
Imagine a first baseman needing a new glove, but time after time, they are only given the chance to buy a catcher's mitt. You'll make it work if you're just having fun with friends, but if money is on the line, I would hope you can get the exact equipment you need...
The limiting factor on competitive deck building is Rare / Mythic Rare availability. Lower rarity cards simply aren’t as powerful, and the availability is high enough for them that they’re almost never an issue.
As you open random card packs, you are guaranteed to open one Rare or Mythic Rare per pack. Arena offers duplicate protection - you will never receive a Rare / Mythic Rare that you already have 4 copies of in a pack. Thus if you already have a complete-but-for-one-card collection, you’re guaranteed to receive that one in your next pack. It also means that there is a maximum number of packs you could need to open to have a complete set of Rare / Mythic Rare cards.
In addition, sometimes your Rare (or Mythic Rare) is replaced with a Wildcard of the same rarity. These wildcards can be crafted 1:1 into any card of the same rarity. This does not increase the rate at which you grow your collection, but does increase the speed at which you can grow it in a particular direction. The drop rate of these is tuned with the intent of allowing a typical free-to-play user to obtain one competitive level deck per card set.
Players in invitational tournaments are granted accounts that have all cards. Individual players are limited by card acquisition, but if you dump in $300 a set you'll pretty much be granted the cards you want, and still comes out cheaper than MTGO.
With the use of Wildcards both from boosters and from the Vault, my experience is that just playing a few matches every now and then is enough for me to quickly acquire the cards I need. I'm sure if you want to be competitive, spending a bit of money for more boosters and a chance at more Wildcards shouldn't be a problem.
However, you can contrast this with Elder Scrolls Legends where, for a few months, I was in the top ~1k players without having spent any money at all. You got plenty of cards as rewards for playing well. You also got a full set of one special card per month as reward for being Legend rank (you didn't even need to reach all the way to Legend).
Imagine a first baseman needing a new glove, but time after time, they are only given the chance to buy a catcher's mitt. You'll make it work if you're just having fun with friends, but if money is on the line, I would hope you can get the exact equipment you need...