Well the issue is that you will likely eventually have a bad luck streak as you play for longer periods of times.
Right, but it's very unlikely that you play for longer periods of time.
There is also a greater chance that you have a very long good streak however this does not matter as martingale will only allow you to make small amounts for each win as you have a good winning streak.
That's the whole point. You accept a smaller profit in exchange for a very low chance of loss.