Yes, this is exactly how WiFi was designed to work. In big cities, the noise floor is so high that frequently, you need one access point per room or two. So, the ability for a client to roam seamlessly is pretty important.
And generally things worked fine that way, back in the day when you could buy WiFi "access points" instead of WiFi "routers". These days, the router function usually gets into the way, though. For many consumer models, you are supposed to be able to selectively disable routing; but in my experience this never works properly. It might seem to work for a day, but then all of a sudden connections keep dropping and become unresponsive. It's just a mode that isn't tested much. And consumer WiFi devices tend to be poorly tested to begin with. Manufacturers care more about rolling out the next cool thing, rather than debugging and fine-tuning existing hardware.
The solution, of course, is to refrain from buying consumer-grade hardware. Instead, you should get semi-professional hardware. I have had amazingly great luck with Ubiquiti's Unifi series of access points. They are not even more expensive than normal consumer-grade hardware. But they simply just work. Put a couple of their access points across the house, and never worry about poor WiFi performance. You can walk all over the house, and you'll never lose connectivity.
The downside is that you'll need a router to plug all these devices into. And ideally, this router should be POE enabled (although, you could use the included POE injectors).
But if you ever wondered how large office buildings make sure their WiFi works correctly, or why some hotels have working WiFi and others never seem to manage; well, now you know. If you spot Unifi access points in the hallways, chances are that WiFi is going to work correctly.