If you have as many as 15 WiFi devices connected simultaneously then your connection for the RPi only gets a fraction of the available bandwidth, which can definitely cause problems, although the extent of those problems depends on the detailed activity of all those other devices. And remember that many devices can have intense transfer activity even when not consciously used by their owner. (eg: Automatic system and app updates, occurring when devices are supposedly idle.) To nail down the causes of your lag can be extremely difficult, especially if you don't have personal control of all these devices yourself.
There is also definite risk of other interference with your WiFi LAN than the normal load of other legitimate users of that LAN. All WiFi networks are subject to physical packet collision with other unrelated LANs using the same WiFi channel. You never see that traffic on your LAN, but the separation is only at high level thanks to the passworded encryption. At low level the physical packets still collide, often destroying each other's integrity. And each time that happens the device which sent that packet must resend it, often after a lengthy timeout (several milliseconds, which is a lot when applied per packet). And then there's the risk of other interference by physical processes that have side effects of high energy emissions including the WiFi band, such as microwave ovens etc.
All in all, it's no wonder that WiFi communication is plagued by problems absent from Ethernet. The great wonder is that WiFi can be used at all with any degree of reliability...
For some people it works very well, especially in LANs with few user devices and at some physical distance from other WiFi LANs.
But in densely populated areas and in LANs with a high number of connected devices, the problems often make fluent media streaming impossible.
Naturally there could be other causes for your media lag too, such as server issues or even some unfixed problems of RasPlex, but the clincher for me is that you didn't have those problems when using Ethernet, which nails it down to a WiFi issue as I see it. Note that this doesn't mean that there's anything wrong with your modem/router, as the many causes I mentioned above can cause such problems even with perfect equipment. The problem lies in the physical nature of WiFi connections, which are always inferior to wired Ethernet when it comes to signal integrity.
If it's only the irritation from the flickering LEDs that motivates your WiFi use, you could try covering them up somehow.
Some other guy suggested painting the LEDs with non-transparent nail lacquer, which probably would work well. (Though I never tried it myself.)
Best regards: dlanor