"you have to pedal faster on a little wheeled bike".
This is true if the gearing isn't adapted to the wheel size. To get the same gearing as with a large wheel bike you need a much larger chainring, or a much smaller rear sprocket (or combination of the two). Or a suitable hub gear setup, which is IMO better suited for small-wheel bikes than derailleurs.
I've done about 53,000 kms with small wheel bikes, mostly 16" on old Moultons then Bromptons, plus I had a 20" Moulton TSR for a while. Kitted out with the Moulton racks, the latter was an excellent on-road touring bike.
The main advantage of small wheels for me is compactness when using other transport.
Mainly trains, but sometimes cars, buses, I've even been on the Paris Metro with a bagged Brompton.
The main downside for me is poorer performance on rough tracks, which is why I sold my Moulton TSR and bought a Thorn Raven Tour.