in terms of percentages, the proportion of adult males that won't fit (too big or too small) 'standard sized' bikes is very small. However a greater proportion of adult women fall outside this range, because average heights are that bit less.
I daresay the big bike manufacturers are not losing any sleep over this; for them it amounts to some tiny fraction of a percent of lost sales, potentially. If they get their sums wrong (and they do) you end up with a load of XXL and XS bikes that have not sold and must be disposed of either at paper thin margins of profit or a loss.
The percentages may be small but that still leaves thousands and thousands of people who find it difficult to buy quality bikes.
The fundamental problem is that (on or off-road) the bicycle just works better if it has bigger wheels. Even over 110 years ago this was reflected in the tyre sizes on offer; Dunlop standardised various 24", 26" and 28" wheel/rim sizes, many of which are still with us today. [For example what we know of as 700C sized rims with a 622mm bead seat were originally sold as 28 x 1-3/4" sized ones. ] In theory the full range of Dunlop sizes allowed most riders to be accommodated; the rims were varied slightly in size so that the rolling diameter of any 26" wheel would still be 26". This meant that you had to decide what width tyres you wanted when you bought the bike, and made buying tyres a bit of a nightmare, too; in (say) 26" wheels, rim sizes of 597, 590, 584, 571 and 559mm all exist (each originally meant for just one width of tyre) and of course nominally 26" tyres do not interchange between rims.
Some rim sizes inevitably became more popular than others, economies of scale kicked in, and folk soon started to want different width tyres to fit their rims. Thus in 622 and 559mm there is a pretty good choice of tyres which fit those rims, even if frames which have these wheels fitted will limit the tyres that can actually be used.
However in the world of MTBs (and as a knock-on, all bikes) things have become worse; 559 wheels are now not so often found on quality machines.
So at 4-11" I think 559 wheels are going to be a good choice. If you want something that looks more like a road bike then 571mm wheels might suit. 571mm rims were originally meant only for 26 x 1-3/4" tyres, but the rim size became adopted for smaller-wheeled racing bikes (with skinny tyres, rolling at about 24.5" overall diameter). At one time there was a good range of tyres available. Today the range of tyres is more limited but (mass produced) new bikes are still being made with this size of wheel and the retailers are obliged to sell tyres that fit them. This means that for the foreseeable future 571mm wheels are still viable, and are usefully smaller than 622mm ones.
IIRC you can buy 571mm wheeled bikes in Decathlon; their XS road bikes (which really are XS) use this size wheel and may fit someone 4-11". Worth a look.
[edit; I just checked and I can find little sign that they still sell bikes or tyres using the 571 size. They do sell a XXS sized road bike using 700C wheels which they claim is suitable for 5'-0" height though.]
Spa cycles have their own frames which are well-designed for smaller folk, but there's only so much you can do with standard sized wheels. I think 4-11" would be pushing it but its worth asking them too.
Chas Roberts has made some wonderful bikes for shorter folk but he is now retired I think.
cheers
