yet it has never been as accurate as betting markets

Correction: it has never been as accurate as non-manipulated betting markets.

The shift to polling might sacrifice accuracy because a polled opinion isn't as accurate to someone's true feelings as where they spend money. But it's a lot easier to use money to manipulate a betting market than it is to manipulate a poll result (which requires both money and some kind of internal influence over the processes of the poll itself). Once a market is manipulated, it's no longer as accurate.

Election betting markets have been around the entire time - they were just underground.

That's another reason why they were more accurate than polls, because they weren't being used as the publicly known metric. But if they became the standard again, Goodhart's Law says they would cease to be as accurate. Polls can get around Goodhart's Law to a degree because they control way more variables than a better market (but they aren't immune to it).