If loot boxes didn't exist - would the associated games still be as popular?

I’d probably say Magic and the Pokémon TCG, though for very different reasons.

Magic has thrived on constantly offering different ways to play the game for different audiences, whether it’s the rotating Standard format, non-rotating formats like Modern and Legacy, “casual” formats like Commander and Planechase, and even game types that turn it into a more board game-like experience, like Archenemy and the standalone box Explorers of Ixalan. That said, the game’s business model does have problems, chief among them being an overloaded product line (something they seem to be working to cut back on) and the looming specter of the Reserved List, a promise from the game’s early days that has slowly made Legacy and Vintage impossible for players to get into in the paper world, and could eventually threaten to destroy Commander as well.

Pokémon has some very interesting stuff going on with its business model; most desirable cards’ prices are kept low by large print runs and constant reprints, both in randomized product and in promotional boxes. It also probably helps that the game is aimed toward kids despite having a great deal of depth, so the tournament try-hards that would destroy the economy mostly shy away from it.