The question seems to ask for several different points in time:
When the floppy based PC was no longer a default option
When application software (games) no longer worked from floppy alone
When PCs manufacturers no longer supplied floppies as default configuration option.
The floppy-based PC, that is a PC without fixed-drive (or other high volume media), booting from floppy started to become obsolete as early as 1983 with the introduction of he PC-XT and DOS 2.0(*1).
This point in time is especially interesting as commercial software almost immediately offered or in some cases even required FD installation, while at the same time games for the PC where next to non-existent.
The PC only started to become a home device considerable after 1985 with dedicated home machines introduced and reaching a sub 1000 USD price level. A good example here might be the Tandy 1000 EX (1987) in the US or Amstrad 1512 (1986) and Schneider Euro-PC (1988) in Europe. Those Machines started out as Floppy only but soon FD options and FD based versions were added (Tandy's 1000 RL being the last in 1991).
So the answer differs according to use case:
Floppy Based systems became
for professional use obsolete ca 1984
for home/game use between 1986 and 1991
Fixed Disk Required
Fixed disk requirement again differs between professional and home use. While it was still possible to use software like Wordstar on a single floppy system in 1985, I doubt that any professional user would still have continued to flipp floppies after generic support of hard drives was added to DOS. Also, more and more software did simply outgrow 360 KiB disks, making it impossible to use it floppy only.
In contrast games were during the mid 1980s often conversions from systems with smaller RAM and floppy sizes. even 'Big' games like Manic Mansion could thus run from floppy. LucasArts Games may in fact give a good guideline here as they were targeted right at the middle of the market:
In conclusion the flip point for games might be quite around 1988 to 1990.
No Default Floppy Anymore
That point in time might not only be harder to pinpoint as floppies never really fully faded, only moved from a dedicated interface to USB based solutions.
Although I had no issue to get a mainstream board with on board floppy interface in 2011 (*2), it became less of an option in the 2010s. For preconfigured systems this has ended a few years prior.
2005 to 2010 seems like a good cut off date for floppies being included with default builds.
I'm asking about the transition, at the cheaper end of the PC clone market, from there being a significant number of flopy-disk-only PCs (containg NO hard disks) to pretty much exclusively PCs containing BOTH hard disks AND floppy disk drives.
This is something that can't really be answered at all, as it very much depends on a force field between
assignment to solve,
available money and
ability to suffer.
I did meet people using floppy based 8088/286 way into the 1990s. Some didn't need more storage, but for most swapping floppies every few pages of text (*3) was bearable, the cost for a new computer not (*3).
With that in mind and for privat/soho the date may be anywhere between 1990 and 2000.
*1 - While there were solutions even before, operating DOS 1.x with large drives was rather painful.
*2 - AMD Phenom II 1055T based, still good for basic use in 2023 :))
*3 - One case I specifically remember was a translator working ca 1998 with a used md 1980s 286 and dual 5.25 drives and WordPerfect.
*4 - As so often updating is as much about the right point in time as it is about money (*5). An update in 1990 would have been rather painless using some IDE adaptor and a low end drive, those components became rare later on.
*5 - An issue most easy to note when looking at CPUs. Christmas 2021 AMD introduced its last series of AM3 CPUs. Prices are way down after almost two years, thus now would be the best point in time to upgrade, as it's quite likely that supply will dry up after this Christmas and prices rising again.