In the 20th century, you could expect a secretary to do this kind of thing (maybe not laundry!), even if it was not strictly company related. I think this made sense for businesses since secretaries were cheaper than you, and some things you have to do on work time - e.g. banking, government interaction, mail.
Now, personal secretaries are all but gone and personal assistants are only really available at board level. So although companies are paying less for payroll, they are losing out since I know phone the bank at work, on work time. I also hate forms and errands, so the company is further disadvantaged by the ego-depletion doing such things causes.
(N.B. I have nothing to back this stuff up, just seems like the way things used to be vs now)
http://www.thelifestylersgroup.com.au/
So, they already exist, you just have to find them. They call themselves a "Personal Concierge Service" so perhaps you could do a search for that in your local area.
Unfortunately, I haven't been able to find something similar when I moved back to Perth.
a) worries about cultural fit
b) they all seem to make the signup process that little bit too painful
c) there's always a slightly offline feel about the process, I want something more web 2.0, on the level of raising a bugzilla ticket for someone to book me a holiday.
There is also the trust issue: would you really trust a stranger enough to do sensitive things?
It just so happened that the previous day when my girlfriend asked me what I wanted for my birthday, I gave her a list of errands to run, people to call, and forms to fill out. She says I should just pay her instead of hiring someone, since she admittedly does do a lot of this crap for me anyways, but something doesn't feel right about hiring my girlfriend to be my personal assistant.
Regarding the business side of things, it might be feasible if you had a central service that could distribute the load of multiple clients among a stable of assistants. You sign up for X hours per week, and you get an assistant on retainer. Maybe you pay a premium if you prefer to work with one person exclusively. Locality could be a problem though, because you would ideally want your assistant to be pretty close to where you work/live.
A reasonably priced non-awful option therefore sounds good.
I'm not sure it's the actual rate of pay. I'd pay $20 an hour for these services no problem, and that's far above minimum wage. The problem is I'd ultimately be paying far more to do all the paperwork, have this person treated as an "employee", taxes, and red tape. If it was just handing cash to someone "under the table" the rate isn't too prohibitive.
Labor laws hurt employees as much as they protect them.
Taking care of taxes and red-tape should be scalable, though, right? Meaning that it should be possible for a company to set all that stuff up and then contract out the people. A consultancy for personal assistants.
New question: is there enough demand and margin to make this worth it for a company to do? Is there enough supply of people who want to be personal assistants? My guesses would be no and yes, respectively.