You have to expect that this will happen a certain amount of the time when you use the "buy the cheapest tool" strategy. Of course, really, it's not "buy the cheapest tool"; it's "buy the cheapest tool that could possibly work," sort of like "do the simplest thing that could possibly work" in agile.
If the tool breaks quickly, that's not usually a terrible outcome. Most companies have at least a 90 day limited warranty you could take advantage of in that case. In many cases, you can even just return the damn thing to the store where you bought it and get a refund or exchange for a better tool. This, of course, assumes that the reason you needed the thing in the first place isn't incredibly time-sensitive, but, usually, it works out fine.
Of course, if it lasts forever, then, great! But, in the intermediate scenario, where you encounter the limitation of the tool a little ways down the road, that's actually where this strategy shines, because you get a chance to upgrade to a better tool without wasting a ton of money on top of the line equipment right away. I know photographers who do this with lenses all the time: they'll rent a new lens for a week or something, go out and shoot it to see how it really works, and then determine whether they want to commit to it. $100 spent on a lens rental has saved some of my friends more than $1000 on glass they don't need. And, if they ultimately do end up buying the lens, that $100 is $100 well spent for peace of mind that they will actually get the use out of the thing that they actually bought it for. And, I think the Harbor Freight strategy makes a lot more sense if you view the initial purchase from HF as possibly a long term rental.
Now, there is that one caveat that you need to buy "the cheapest tool that could possibly work." If you're a professional machinist, for instance, don't go buying a $5 caliper and thinking that will be good. Go and spend the $150 or whatever on a Mitutoyo instrument to begin with, because you know damn well you will need it. This is just an example I pulled from personal experience, as I needed a caliper for hobby purposes a few years ago and ended up looking at things ranging from that $5 caliper on up to precision instruments. For my purposes, the low end is totally fine, because I don't need accuracy better than 0.1mm, and it's not my professional livelihood on the line. But, if you're a professional, never trust an instrument that doesn't come with a certificate of calibration.
I've also used this strategy with good success on photography equipment, myself. I wanted a DSLR camera I could use to take pictures for hobby purposes, mostly intended for web use. I did a little research and decided that a used Nikon D3400 was for me. So, I went to eBay, found one that only had about 1200 clicks on the shutter that came with the 18-55 kit lens and the original box for $325 (tax and shipping included), and I bought it. I augmented that with a used 90mm Tamron macro lens for under $150 and I was good to go.
It has one or two small limitations that either only come into play outside of the original use case I had in mind, or which aren't really annoying enough to mention, but, for the most part, it's been a spectacular camera that I spent under $500 on, as opposed to spending $1000 on a Z50 (or, you know, gone really crazy and gotten a D850 or a Z9), and then another $900 on a new Nikon 105mm macro lens, but, for my purposes, I can take photos that are 95% as good as what I could ultimately produce with the more expensive equipment, but, I can legitimately say this strategy has saved me over $1000.
I did exactly the same thing when I started learning to play the cello. A new, carved wooden cello suitable for a student probably runs around $2000-2500, and that doesn't necessarily include a decent bow. This is also an instrument one will certainly grow out of if one continues playing. I did my research and went out and bought a Yamaha electric for $3000 and went to a cello shop to try out bows, ending up with a nice $1200 bow. I ended up with an instrument I'll never outplay and a bow that will last me years. The alternative would have probably been a much less playable bow and instrument, or a lot more money expended.