When those disposable multi-blades were getting too costly for my taste, I just got my father's old safety razor out of storage, purchased a packet of 10 Wilkinson blades for it at ~2-3€ and still haven't used those up today.
Seriously men, do away with the cheaply made but expensive plastic trash and invest once in a nice safety razor. It's worth it.
I reuse the multi blade ones for quite a while - months each. They stop working because the blades get junk between them, not that the blades get dull. To remedy, strop them backwards along your arm to clean the junk out, only a few times seems necessary, then give a rinse under the tap. I just do this out of habit each time I use them now - they last a long time.
If everyone knew and practiced this, the razor blade industry wouldn't be a billion dollar industry. People would buy an order of magnitude less blades. The maintenance takes less than a minute, and is only necessary once every two weeks (if you're a weekly shaver). As you say, stropping will make the blades good for months.
If you are using feather blades, get something that isn't sharper than a scalpel. If you aren't using feather blades, you are pushing to hard, in fact you shouldn't be pushing really at all.
Are you talking about a safety razor[0] or a straight cut razor? I also switched, and find I cut myself a lot less than with a cartridge razor. If I do cut myself it is usually not so deep. The cartridge razor I used was Gillette Fusion, so not a cheap brand.
Are you sure the blade is properly tightened? My Wilkinson requires some force to properly tighten, slightly bending the blade, at which point it's firm, sticks out less, at a different angle, and it's not as easy to cut myself.
Other helpful tips - let the hair soak for a couple of minutes; clean/dip the blade with >90% alcohol to remove moisture, preventing corrosion and dulling. Haven't had issues shaving since.
Honestly, you've got to be doing something wrong. Maybe a bad, non-lubricating shaving cream, way too much pressure, or inappropriate holding angle. Safety blades are not known for creating horror films.
If the motion of the blade is perpendicular to the edge of the blade, it shouldn't cut you no matter what angle you hold it at (some angles will cut your hair properly but none should cut your skin.) If the motion of the blade is parallel to the edge of the blade, then you're going to cut yourself.
It's not like other people have armored skin that's immune to sharp things; we all cut just as easily as you do. It's a matter of technique.
Have you tried various blades? People swore by feather but I found those too be too stiff and sharp. I absolutely hated them. I tried Astra Platinum and they seem more flexible and provide a much better shave for me. There's a "chart" out there that lists various brands from sharpest -> smoothest
Yes, I have, and yes, my latest have been Astoria, and yes, I pull, instead of slicing, and yes, I've futzed with the angle, and yes, I've tightened the razor, and yes, I've played with not tightening it as much, and the end result is that despite all this work, the disposable plastic crap is easier and less painful.
There's a reason for why the world has switched to the disposable plastic crap - and its not because people are fools. It's much the same reason for why the world switched from horses and buggies to automobiles.
That's really interesting - I've cut myself a few times but mostly just due to impatience or a new blade. But my face also doesn't require daily shaving so I don't mind taking a few extra minutes.
As a huge fan of safety razors you're one of the first people I've heard argue against them.
That multi-blade crap tugs my beard hairs and give me irritation and ingrown hairs. I just use a trimmer now and don't bother with jobs that need me clean shaven.
I wouldn't want to go too hard on this, but there is something a-moral, if not immoral in shifting the apparent cost line, but actually putting the consumer into pay-more outcome. Up in the budget planning space for tech we often do the opex vs capex thing, and it is clear we have to be very specific what window in time the capex/opex is expected to equalize or show some benefit. Otherwise, you can incur opex forever, and pay a lot more than the capex (yes, modulo the non-obvious costs of operations for owning the capex)
But nobody does this for razors.
Terry Pratchett had a good one-paragraph rant on expensive shoes vs cheap cardboard shoes, the expensive ones last 10 years the cardboard 10 days.. its in the same space.
Gillette sold their razors at 1/4 of the manufacturer's cost but they had a patent on the razor itself which will only take Gillette's razor blades.
Those razor blades are markup 400% - 1 cent sold for 4 cents.
The "innovation" was people are willing to pay per shave instead of paying upfront for a razor which was seen as an investment at the time.