Using NVMe SSDs over SATA SSDs in basic servers is an awkward sales pitch
We have traditionally mostly bought basic, inexpensive 1U servers, almost all of which have had either two or four drive bays. Our transition of these servers from using HDs to using SATA SSDs was relatively straightforward. It was driven by dropping SATA SSD prices, the clear improvements in performance even for casual activities like installing the operating system and upgrading packages (and rebuilding software RAID mirrors), the probable increase in service lifetime, and how relatively easy it was to substitute a SATA SSD for a SATA HD (except that for a while that was a hassle, which slowed down our transition).
Putting NVMe SSDs in such basic servers with only a few drive bays is reasonably doable in terms of PCIe lanes and space. Even if you support four NVMe SSDs, that only needs 16 PCIe lanes, the M.2 form factor doesn't need much space, and people have accepted non-hotswap drives in 1U servers before (our Dell R210s have two non-hotswap bays). Or you could go with the U.2 NVMe form factor; as noted by Andy Smith in a comment on my entry on SSD versus NVMe for basic servers today, Tyan will already sell you a 1U server with 4x U.2 and 4x 3.5" drive bays (here's one model).
However, actually getting people to do this seems like an awkward sales pitch. Right now you'd either pay more for a U.2 SSD or probably live without hotswap for an M.2 NVMe SSD, and while you get much better IO performance, relatively few basic 1U servers are doing things that are IO constrained on SATA SSDs. If you're using SATA SSDs, you're getting the durability advantages of solid state storage and probably most of the power and heat savings, and you've already taken the first massive leap from HD performance.
What feels to me the most likely path toward NVMe on basic servers is the spread of machines like Tyan's model, with 4x U.2 and 4x 3.5" bays (at competitive prices against basic 1U servers if the U.2 bays are empty). We and probably many other buyers would almost always use SATA SSDs in the 3.5" bays, but if U.2 SSDs became competitively priced we would probably start switching to them (if nothing else, we wouldn't need adapters). The existence of these servers with the option of U.2 might act to drive down the price of U.2 SSDs by increasing the market (we can hope).
(Having the option of either 3.5" bays or NVMe bays seems smart, because HDs remain your best option if you want a lot of disk space in not much physical space or cost. You can now get 4 TB SATA SSDs, but they're quite costly. Meanwhile, 8 TB HDs are a few hundred dollars.)
Another option is that makers of basic servers could make very short servers that use M.2 NVMe SSDs on the motherboard in order to save internal space. Dell already did something like this with their half-length R210s, which had non-hotswap drive bays because the drives were mounted sideways to save depth. However I'm not sure how much of a priority rack depth is for people these days and we certainly found that having a mix of rack depths could be awkward. If these servers were the inexpensive option, we would probably buy some (assuming M.2 NVMe SSD prices for small sizes stay basically the same as the same sized SATA SSDs).
All of this leaves me expecting that any transition of basic servers to NVMe for us will be every slower than our transition to SATA SSDs, which took way more time that I expected (we more or less started in 2013 but as late as 2017 we were still using HDs in some new servers).