I have seen variations of this same approach discussed previously here.
Statistically, it sounds very sensible, and in keeping with the humans' natural desire to measure everything in periods, be it days, weeks or months or years. Which, of course, is also useful for comparative purposes. It probably has some benefit from a psychological aspect, too.
But, on the other hand, markets do not perform so conveniently as to match our human cyclical, periodic desires. A poor performance one week compared with a previous week is not necessarily a reflection on the trader's own performance, rather it perhaps due to a more erratic or sluggish market environment.
In this light one could argue that if, for example, one has a 4 win/2 loss situation why stop there, if the market is apparently working favourably? And, again, if one unfortunately starts off with 2 losses, then to stop there might result in missing opportunities to recover later.
Personally, I prefer to manage risk and money by applying rules to each trade individually rather than in bulk numbers of trades. And then to select my trades according to the quality of each signal setup regardless of how many or few trades are taken per period.
If one's trading strategy/method has been selected/developed/tested in order to provide a probability edge over a number of trades then I don't see any reason to need to stop trading for the rest of a given period just because one hits a level of 5 wins or 2 losses in a pre-defined time period, whether it comes at the start, middle, or end of that period. It is surely the quality of each trade setup that matters rather than the number of trades?
Having said that, I also tend to behave at times in the same way. For example, if I get to the last few days of a month and I am happy with the results so far then I do reduce the number of trades and risk exposure to protect it - illogical but human, I guess
But it is good that you raise the subject, because this issue is important for every trader to think about and decide which approach works best for them.