Correction: you can usually run 10Gbit/s over CAT5e if the cables are not too long, so you probably won't need to replace your cables. But the hardware is indeed expensive.
That isn't a correction, that is pedantry. Nobody is going to spend $100/month and thousands on equipment and then run their 10 Gbit/s network on 5e. The lengths to remain stable won't even bridge floors of a home let alone from end-to-end.
If it was free in terms of equipment, you might have a point. Since then 10 GB is just a "bonus" but it isn't, or even close. So you'd be cheaping out on the final 10% of the cost.
> The lengths to remain stable won't even bridge floors of a home let alone from end-to-end.
This isn't true. I've run 10gbit over cat5e many times in 10-30m lengths. That might not be enough for end to end on your house (although it is for many peoples), but it's certainly fine between floors.
10gbit switches are becoming significantly more common. Vendors like fs.com and even Netgear offer some reasonably priced options. Mikrotik and other vendors offer better (pricier) options, but assumedly if you want 10gbit (or even 1gbit) you're an enthusiast or business anyway.