Incidentally, in blackjack games, you could argue that martingale is slightly more effective than flat-betting, since you are more likely to lose with excess low-cards, which would raise your odds in subsequent rounds.
Edge in freebet BJ, my preferred version on Live Casino (free double downs and splits), is actually about 0.8%, if I take the expected RTP of 99.2% at face value. Very close to traditional crypto dice.
You're right of course, as the shoe gets dealt out, you do expect better deals as martingale progresses on a bad start from a new shoe (which is when I get tempted to martingale).
That said, I tend to do my martingale on the dealer bust sidebet, and only once dealer survives 3 or more consecutive non-bust hands. That's only because of rough estimation that dealer has about 1/4 chance to bust, AND because busts of 4 or more cards gives increasingly better payouts. So it's netted me some great wins in long sessions -- hitting a 6-card bust when you're high on martingale feels awesome -- but across 90+ days, you can easily keel over on 10-hand no bust streaks if you don't start with the min bet.
Potential problem is with live freebet style, you can't stop other players from continuing to hit or split on terrible hands (it's a single player hand, and if you stand, dealer continues to hit/split for whomever else chooses), thereby messing about with potential dealer busts. Probably doesn't matter end of the day, but in some sessions, you always get that one guy hitting on hard 20...