Why either Ltd or umbrella?

[Criticular]

Apologies if the question is too naive and theoretical but I still want to know the answer. As far as I can see contractors are usually offered to work through ltd or umbrella (or just umbrella). But did anyone try to work as a sole trader and why this is not an option?
One thing is the sole trader is responsible for any fault with all his property but assuming he has a right sort of liability insurance what else stops contractor to work as a sole trader?

[Maslins]

Main reason sole trader isn't viable for contractors is risk for end client.

Umbrella - all taxes done via payroll (oversimplifying, this is the "high tax" route)

Ltd Co - director decides how to operate, whether IR35 applies. If they decide it doesn't, this virtually always leads to lower taxes. If HMRC later decide this decision was wrong (and win), it's the contractor's Ltd Co which pays the extra taxes (NB this is different for those in the public sector, and planned to change for private sector too from April 2020).

Sole trader - director/client agree whether employment or not...but if opting for sole trader invoicing, suggests they believe it's not employment. If HMRC later decide this decision is wrong (and win), it's the end client that would pay the extra taxes. They're typically not prepared to take this risk, hence insisting contractor either sets up a Ltd Co or works via an umbrella.