I'd like to begin with a full disclaimer that I am not a representative or part of any casino, so I am most certainly didn't know how exactly they work and why, and my answer is completely based on my assumption, at least, "assumption", as it's hinted here and there the why they does so on several threads. [Maybe Kirito89 can confirm my assumption below, as per his own platform's policy and system?]
Though it'll be very ideal and nice if it can be actualized, the why they didn't catch multi-acc abuser right away from their first bet, or even straight from the first time they sign up, is because it'll be a huge waste of effort, or a very expensive ones, to filter out users right from the first time they sign up. I assume there must be a good amount of user signing up on daily basis. To manually check them one by one through so many filters in matter of seconds before sending them a verification email will be... fun. Not to mention the false positive.
So instead, they developed and perpetually fine-tuning a fraud detection system that flag users through several parameters, so these multi-acc abuse detection is not an instant matter. Instead, it's a process that happens and verified gradually [to prevent false positive] through several filters while the abuser playing in the said platform.
I can confirm that identifying multi-accs on the first bet would be a huge waste of effort and resources. And while the process of identifying them is mostly automatic, it also requires a human interaction to analyze and confirm the data, like holydarkness said to prevent false positives, and also to confirm the data is accurate.
What I can also confirm 100%, when we do find someone multi-accounting, as long as they don't engage in lets say dishonest activities, resolutions are always in the player's favour.