I don't get the why you feel you should be competitive without paying. This is a free to play game, also known as a pay to win game. You shouldn't be surprised when you get outgunned by someone that has a .50 cal, while you're toting a .22LR. They paid for performance, you didn't. You can either pay here, or pay on MTGO.. but either way, you're going to pay.. be it in time investment or cold hard cash. To expect to be able to be competitive without spending reeks of entitlement.
It was fine to go on the ladder for free when the game was new bc the power level was pretty low. That's not the case anymore.. the gap between the D cards and the rest of the library has widened significantly. But regardless.. no matter which form of Magic you choose.. Wizards is gonna get a little out of you.. or you can do horrible, tedious things like play against the AI.
As someone who started a year late and has since been able to get completely caught up with very minimal spending ($35 total), I don't even really think this issue is THAT bad. At least currently.
Should you be able to stomach grinding against the AI enough to be able to buy an entire set (likely KLD at this point) you should have enough cards to put together at least a couple of decks that will be perfectly viable online. They may not be completely optimized, but they should still function well enough to win games.
I will concede that doing so leaves you with a very limited amount of decks/archetypes you have available until you are able to unlock a significantly larger portion of the cards though. Unlocking all of KLD for example will give you at least a few viable Aggro options by itself, but will likely leave you struggling if you are trying to build a control deck off of it alone.
I will also concede that grinding out everything for free takes a significant chunk of time and only stands to become worse should the game continue to receive support. Which as you pointed out is generally just how F2P games operate.