Many do (I know I do) - but also we should consider how many people are in contrived "self employment" - I mean people like delivery drivers who are supposedly self-employed business but yet work for one delivery company, in uniform, in a branded van (that they have to supply). Of course they're not really, properly, self employed, but the companies insist on them being so, thus saving employers NI etc. (and, if they pay themselves in dividends, the workers also save NI)
There are 4.2m small businesses in the UK with 0 or 1 employee - that's something like 3/4 of all SMEs. Some will be bona-fide Self Employed tradesmen etc, but I'm sure there's a large number of these that are - to all intents and purposes - actually employees.
I've said before, a really simple change would be to abolish NI and raise Income Tax. At the moment, only employed working people pay NI, which seems pretty unfair to me. Although I would lose, personally, if such a change happened - I think it's the right thing to do.