My 20 quid router is still going strong after 10 years.
I suggest price is not a reliable indicator of capability or quality. Though or full disclosure, I only have about 4 things hitting it up for Internet access.
Let us be clear about what we mean when assessing the capabilities of this and that AP/router to "handle" a certain number of devices. There's two aspects to this that I think we should tease apart:
Firstly, there's purely the Wi-Fi ability. How many clients can the AP service concurrently. When planning big systems, I start to get nervous when this gets to the order of 20-30, though that's mostly about the service performance delivered rather than the concept that the AP "couldn't cope." Though I've seen it go higher. (Caveat, this is enterprise kit I'm talking about.) I would be very surprised if even cheap SOHO kit couldn't handle 10-15 clients, but if it's a matter of concern, then we ought to be checking the datasheets.
Secondly, there's the ability to handle the Internet traffic, particularly the capacity of the NAT and the firewall. This affects both wired and Wi-Fi devices alike. AP's don't do NAT/firewall, this is only something your "edge" devices connecting to the Internet has to handle (ie your router, whether it's Wi-Fi is enabled or not.)
For NAT and SPI firewalls to function, they have to monitor the sessions passing through the NAT/firewall to/from the Internet and build various tables in RAM (usually) that maintain all the port mapping and so on. The more devices you have, the more sessions that they want to open, the more sessions need to be maintained, the more RAM required and the more powerful the processor needs to be to run it all.
Unfortunately, in most SOHO kit, information and statistics about this sort of thing is not available in the UI (and certainly not configurable.) Maybe pro-sumer kit like Draytek, Ubiquiti et al might offer it. Even if it were available, I suspect for most (lay) people it would be unintelligible even if it were available.
I submit that discussions about such things are little better than guessing, if we are being honest with ourselves, in the absence of any information from the manufacturer, stats. from the kit, or some objective and methodical test regime.
If would like an anecdote dear reader, years ago I had a SOHO router deployed on my "guest" network "at work." Despite it's paltry 16MB or RAM, it was fine until numbers of devices got upwards of about 70-80 whence it would crash regularly. We replaced it with a low end "proper" Cisco router (with an ADSL interface) and half a Gig or RAM (not to mention access to more stats than you could ever wish for) and it was fine for years afterwards.