Actually....I think there's quite a string of issues with the razor(s)
1) I think you called out the main 'flaw' in the design when you mentioned the 20 razor cartridge inside the razor that could well be exposed to water over a few months.
2) In addition to that having a head on a razor, with a blade loaded into it, that requires you to bend the head into shave-ready form every time you use it - and then bend it back after the shave - could also very well lead to some accidental finger cuts if you're not careful.
3) The shape of the handle is basically a rather short, rectangular rod with pretty pronounced edges - it would not be my first design concept if I were to design a handle myself as it's not quite as ergonomic and pleasing to hold on to as many modern offerings.
4) It's not what I would call a well-balanced razor. Too much towards the body forcing a stronger, conscious effort to get the head-angle correct.
5) Using proprietary blade magazines is tough way to sell a product
I don't know if any of these 'challenges' caused the end of the repeating razors but if I look at the continuation of the Schick razors as they moved to injector razors a lot of the above seems to have been addressed in subsequent designs.
I do of course still love these things but I wouldn't call them anywhere near 'perfect' - maybe 'quirky'

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