I can't imagine....
....letting a user pick their own machine, even the most savvy ones will bring something that's just a mass of inconsistencies, I can appreciate the idea of letting them have their own machines and saying "your pc, your problem" but the simple fact remains that HP customer support (or acer customer support etc etc) won't provide support for any bespoke software, and from my experience, bespoke software is what screws up most of the time, hardware fixes are relatively rare where I work.
Because of this, it's pretty likely that your IT team will need to be nearly as big, but customers will still have to liaise with their manufacturer. Which is similar to my workplace now; We do everything, if something breaks we tell <provider> to send us a new part, or send them the whole laptop if it's the motherboard.
I can only really see this working well in a smaller business that doesn't do anything particularly fancy with their machines, but from where I'm sitting, I see a 4000+ users who would buy the pretty looking one and come knocking because none of their software worked.
Interestingly, all our laptops are fancy looking brushed aluminium jobs with terrible build quality...so maybe it's not just end users who make poor decisions on this.