In terms of startup ideas, there is probably an Uber like service opportunity here. An app where your "operators" can download and put on their phone, and when ever they want to they can put them selves "active" at which point you will route calls to them over your VOIP network, they take calls, record the data (name and number). You pay them per hour to be on-call, your customers pay you per call, and for infrastructure you need an enterprise account with a VOIP provider, a web site, and a way to accept payments. (That might be what Answer America is doing, I don't know but it seems pretty doable)
It sounds like a good idea in theory, and excuse my being unimiginitive, but answering services are even more blue collar than ride hailing. It's a lot of work that I'm not sure many people want (the operators and everyone else involved with running the service).
Anyway, the big problem with this concept is the profitability of answering services is predicated on constantly changing the rates and dropping "dead weight clients" (that is an industry term from the guy who facilitates answering service sales). I don't know if this is possible in an uberized answering service.
Would answered calls be worth enough that people would pay a higher rate during higher demand periods? I honestly don't think so.
The industry could stand some innovation - it is severely lacking. Why is it that 70% of all answering service sites are not served with TLS?
(hint: proprietary answering service equipment vendors have choked the industry and now it can't innovate)
I don't think you're being unimaginative, you're asking good questions.
There are a two things which are orthogonal here, one is capturing what might be called 'fractional GDP' from available workers. Basically that is ways in which people are creating an easy way for an individual worker to work or not work based by creating a disintermediated interface between the service users and the service providers. The 'App' economy, the 'Gig' economy, what ever you call it, it tries to create a lightly held employment relationship between service provider and client in the form of an application and a payment provider.
The second thing is whether or not there is enough value in a telephone answering service that it can be successfully monetized. That is an operational efficiency question which would depend on some research into the hows and whats of implementing such a service. Customers for such a service go from the rich and famous who might go so far as to hire a staff member to screen their calls, to someone who has never considered it. Using existing infrastructure and full time staff clearly hits a minimum cost point, and then folks like the author of the essay don't get enough value to hire the service at the rates they need to charge.
Bottom line is if the service can be restructured in such a way to be additionally more efficient such that you can capture the low end of the market and perhaps serve the upper end at a better rate. If you can that is a business.
In terms of startup ideas, there is probably an Uber like service opportunity here. An app where your "operators" can download and put on their phone, and when ever they want to they can put them selves "active" at which point you will route calls to them over your VOIP network, they take calls, record the data (name and number). You pay them per hour to be on-call, your customers pay you per call, and for infrastructure you need an enterprise account with a VOIP provider, a web site, and a way to accept payments. (That might be what Answer America is doing, I don't know but it seems pretty doable)