I do similar work. I don't always find that inbound startups and founders know as much about how to really do an "MVP" as their using the language of Lean Startup would suggest. There are certain pockets in major startup markets that do understand the language, but in those cases you're more likely to find a technical co-founder who does this work.

The biggest challenge in a business like this is going to be your business development and deal flow (i.e. "gig flow"). Yes, it's a compelling concept, but it's going to be all about keeping the gigs flowing and as a small shop the biggest challenge is going to be doing enough business development work while also doing the production work yourselves. I have done a lot of thinking and work about this for freelancers, myself included. I have some good solutions if you'd like to chat about it.

Either way, the success of your execution is dependent on the quality of your knowledge capital I.e. What you execute on. Getting out of the building may require a combination of skill sets which you may find more readily available in some places versus others. Ultimately your most important partner is your customer - execution skills you can get anywhere...

This entirely depends on the size and funding level of the startup. I find that many don't have the capital to pay for an outside firm to develop their MVP and instead would be looking for an in-house technical cofounder who would work for equity.

Ones that can afford this model are very happy indeed to have an outsourced team to handle everything for them.