That said, I can't help but think the following:
1) Before software, there were already products and services.
2) Software came along, and was used by people providing products and services. In a way, this was already PaSH, kind of, just more indirectly and it wasn't called that as the emphasis was on the products and services provided, and not the software.
3) Software began being provided by "application service providers" (ASPs), which sort of evolved into SaaS (software as a service). We even sort of commandeered the term "services" as an abstraction over software/business services as in "web services".
4) Now we are talking about "software", plus the old meaning of "service", where the two are fused into one.
It's a new word (but not really a new concept) for a somewhat more recent organizational form ("service based organizations").
In particular this middle ground can actually help support a SaaS app until it reaches some level of critical mass. The early days of a PaSH app is about risk mitigation. A later stage company can use it to drive revenue up.
It's definitely not new, but it is a model I'm seeing more and more small team SaaS operators adopt.
Customers find it valuable because it ends up being a form of low cost, optimized outsourcing.
The most interesting thing to me is the potential revenue difference between just a product and just a service.
For example, take something like Shopify. They are purely a product, they charge $79 and it's totally hands off. If you were doing a custom shopping cart or whatever, you might charge $5,000 or something to build/cusotomize a solution.
There is very likely a place where you could run someone's store for them for like $500-1,000 a month without them having to touch anything. You could hire and train someone to run these stores and each person could run say 100 stores. That is 50-100k per month per person running those stores.
It would not be super difficult to find that many customers and be able to pay people to service those customers well. The outcome for said customers would likely be better than if they had to manage it themselves, but it would be a lot better than what most build and move on type consultant type arrangements would provide.
The same idea applies to a lot of niches, not just e-commerce. I suspect there will be a lot of offerings that pop up in the next few years that do exactly this.