OP, you can definitely think of this as a separate strategy because it is impossible for a gambler to stop in time and only those who can make this impossible possible can succeed in gambling. After three consecutive wins, a gambler should definitely stop gambling for a while. But instead of stopping, many gamblers start betting again, and thus a gambler forgets that he should have stopped in time. This strategy is certainly difficult for a gambler to master and can certainly be called a strategic quality.
I think what the OP said has a point, but it heavily depends on personal limits. Some people might stop immediately after a big win on their first bet, while others would stake some of their winnings again. On the other hand, sometimes gamblers have a kind of belief, when they win three times in a row, they're convinced it's their lucky day. I don't think anyone with that kind of belief would even consider it the right time to quit, they will even think otherwise to bet all their budget. In many cases, we also often see people forgetting to withdraw their initial capital when in a winning position, although I believe that there are gamblers who are able to stop in time, regardless of whether they are in a winning or losing position.