In my opinion there are really just two "problems" with short scale basses:
1) Many short scale basses are entry-level models, seemingly aimed at beginners, or to be an extra, "fun" bass for long scale players. These are the models that give short scale basses a poor reputation. If you want a short scale bass as your main instrument you should spend the same (or more) as you would for a good quality long scale bass. Avoid the cheapest models, most of them are more like toys, or practise instruments for kids (or maybe modding platforms at best IMO). But a GOOD short scale bass can be every bit as good as a long scale bass. At least if you also find strings that work for your playing style...
...which brings me to:
2) On a short scale bass there's a VERY fine line between too light gauge strings (causing fret buzz unless you play very softly or raise the action) and too heavy gauge strings (causing weird "out of tune" overtones in higher frets, particularly on the lower strings). If you go any heavier than 45-105 the tone/intonation in the upper frets will start to suffer. But 45-105 on a short scale bass will feel noticeably lighter than 45-105 on a long scale bass. The choice of decent quality short scale strings is rather poor, unless you prefer relatively low tension strings, and a supple "feel".
If you're used to playing 40-100 (or lighter) on a long scale bass you should be able to find strings that will work fine for your playing style on a short scale bass too. But if you're used to 45-105 hex core (or heavier) on a long scale bass, and want to be able to dig in relatively hard (fingerstyle) without excessive fret buzz, the choice of decent short scale strings becomes extremely limited. You may need to adapt your playing style a bit, and maybe also raise the action slightly higher than you're used to. The best choice of strings will of course depend on your playing style, what kind of music you play, and what type/gauge of strings you're used to on a long scale bass. But some of the short scale strings you find for sale are UTTERLY USELESS, no matter what kind of music you play. Rotosound short scale strings are probably the worst strings you will even find (and I love Roto long scale strings). I honestly don't understand how anyone can play the short scale Roto 66s. They're too supple/loose to even hold a steady enough pitch to tune them properly! And unless you play them with a feather (or raise the action sky high) they will buzz like crazy. I can't believe they still sell this junk.
I think it's also worth noting that the stiffness of many (but not all) flats can be a good thing on short scale basses. I can only think of ONE type of roundwound short scale strings that work for my playing style, that I also like the tone of: Pyramid Pure Nickels 45-105. With flats I can think of at least three different types that I love on a short scale bass: Pyramid Golds, LaBella DTFs and D'Addario Chomes. In fact, Chromes are a very good example of what I'm talking about. I absolutely hate them on long scale basses. I find them stiff, unresponsive, inarticulate. But this extra stiffness means they work much better for me on a short scale bass, where the stiffness compensates for the lower tension. But this is of course for MY taste and MY playing style. The best choice of strings will of course always be very subjective.