In many real world scenarios I have found Power over Ethernet to be extremely lackluster. Even with mid-range office installations there were still problems with VoIP and intermittent packet loss in relatively smaller homes. The main problem with people who have poor WiFi service in their homes seems to be due to:
1) poor placement of the WiFi router in the home (usually connected in the garage, or on top of a gigantic metal file cabinet for some outlandish reason)
2) physical barriers such as concrete and metal that cause RF signal noise and other hiccups
3) over-saturation of the WiFi channels without adequate WiFi channel switching in a densely populated area.
Some of these issues can be resolved by having the ISP move the modem to an area where the WiFi router be ideally suited to encompass your entire home. However, if like many people, you ran PoE because your WiFi signal just didn't seem strong enough, I believe I have some bad news. Like many technologies such as "WiFi range extenders", PoE is very much a "quick fix".
There is something about PoE where, depending on how your home is wired electrically, seems to be hit or miss. If it seems to be working for you now, that is good, and I'd leave it be. However, if you're thinking about going fully wireless, you may as well install a self-maintained wireless mesh network in your house. I would not recommend anything else, even if you already installed PoE devices to improve your wifi signal range. Basically, PoE has always been a bit of a "hack" in my opinion. PoE became very popular in office environments to minimize the use of wiring, when wiring itself was already becoming out of date. The same goes for range extenders, which essentially are repeaters that screw up your connection when you jump from one to the other on the same SSID.
Fortunately, what became mainstream in the last year and half is the type of WiFi mesh network required for full coverage of a large area. In the past, these were 1) not affordable and 2) not generally available to non-corporate non-enterprise customers.
While advances have been made in PoE for throughput, far more advances have been made with WiFi mesh. If your home always lacked adequate WiFi signal, I would strongly recommend using Google Wifi or the Eero mesh networking systems. You would have few problems, if any, and its advantageous to you, because you will have near zero signal loss in your home if the placement is done correctly. Furthermore, you could use your existing router in bridge mode for physically wired connections. In ideal circumstances you will always want workstation computer systems and VoIP phones to be run directly through Cat5/Cat6. This is because there is still a slow down when you run over WiFi and the possibility of packet loss. But if you have a lot of wireless devices, including smart TVs, tablets, and cell phones running through your house, I think you will really want to consider a WiFi mesh network.
I look at this issue often, and really, I think this is the best possible situation when it comes to ridding yourself of WiFi problems. Power over Ethernet, to me, has never really cut the mustard, but I'm sure others will disagree.