Last bit first:
Many people do the majority of their work through umbrella companies but have additional employment 'on the side'. HMRC have no idea whether you did any such work and therefore need you to complete a tax return in order to declare any earnings from outside of the umbrella company. (They also need to know whether you've made any money from investments, etc, which would also not show up on the figures from the umbrella company).
Main bit:
The 'u', in UTR, stands for 'unique'. It means that the taxpayer reference applies to one, and to only one person. An individual can't have two UTRs and groups of people can't share a UTR.
For example, Alf might run several 'sole trader' businesses, such as running a small cleaning agency, designing web sites and working as a market trader. However he only gets one personal tax allowance (which is linked to his UTR), so he can only have one UTR and must declare all the earnings from his various businesses using that UTR.
If (as your post suggests), Bert, Charlie, Dave, Eddie and Fred were to agree to declare all of their earnings solely through Bert's UTR, then:
(a) the collective would only be allocated just one personal tax allowance, instead of five, meaning that they'd pay MORE tax ;
(b) their collective incomes would be seen as a very high income from a single person, resulting in a HIGHER rate of tax being charged upon some of their earnings ; and
(c) Charlie, Dave, Eddie and Fred could be fined for not registering their businesses AND for not submitting individual tax returns.
Registering as self-employed (and thus acquiring a UTR) is a simple, if somewhat tedious, business. Completing an online tax return is remarkably easy. (It's not much more difficult than, say, completing an order form for something from a web seller). Why complicate things???