They don't reshuffle every time because your last statement is very wrong. The money card counters can take before being caught is a rounding error in the face of the masses of people who are happy to play with no edge.
But yeah, it's really easy for casinos to keep a track of your betting pattern and kick you out if you're playing the game too well. That's why the really successful card counters play as groups with personas. They'll station a bunch of low key guys around the casino and have them maintain a steady stream of cheap wagers while they count. When a table gets hot they'll signal a flamboyant high stakes looking guy to sit down and play a few rounds.
The Casinos will eventually catch those guys too, simply by correlating who is sitting at what tables when the high stakes guy comes to play, but it takes a lot more work and they make out with a bunch more cash. Worse, because what they're doing isn't illegal the casio can't even deny them the winnings, only kick them out and plaster their faces all over the blacklists the casinos use.
However, casinos now know of and how to foil this strategy. The countermove is to prohibit entering a table while a shoe is in progress. Either the new player must wait until the deck reaches its established end point at the cut card, or the deck gets reshuffled immmediately upon the new player entering. Either way, an incoming player can't take advantage of any count.
They sucked most of the fun out of video games to turn them into gambling machines for kids. Now imagine if they sucked the remainder of the fun out, and the only thing left was the gambling. Now you can only have fun if you think playing a game where you are statistically guaranteed to lose everything in the long run is fun.
They may have more glamour in the gambling-centric cities, but the few casinos I have been in have all been sad, dingy, smoky places filled mainly with old women staring at their slot machine with dead eyes and cups full of their pension funds.
Even if you temporarily win at gambling, you're still part of a machine that sucks life out of people and leaves them drained husks.
If you don't have an expert system mathematically guaranteed to give you an advantage over the house, you're better off gambling on the stock markets, because at least if you lose there, it might have at least paid for someone else to have a decent non-bullshit job for a little while, and there's also a possibility that everybody wins, even those who didn't play.
In Quebec all the lottery games and the casinos are owned by the government, thus every gain there goes to the public sector. Everyone win (except the one with gambling addiction, which are sadly the vast majority of the customers).
Blackjack is an incredibly boring game, remove the ability to count and beat the odds and no one would play it.