The half effect of the combination of wireless extenders is very interesting, which I was not aware of.
That's because bandwidth is required to maintain the extended network. This would be true for non-Apple routers as well. Mesh networking can overcome some of this by using a dedicated wireless backhaul for this ... but even Mesh cannot beat performance of either an all wired network connections or using an Ethernet backbone with wireless access points. The latter would be something like: Cisco AeroNet or Ubiquiti UniFi
Some mesh networks that utilize dedicated wireless backhaul are: Asus HiveSpot, D-Link Covr, Linksys Velop, & Netgear Orbi.
However..... when I disconnect the Apple Airport TC and even the 2 Apple Extremes (extenders), and just use the modem that has its own WiFi, I still get the same slower speeds inspite of being right next to the modem.
If that's the case, then adding the Apple equipment will not make it "better." There must be something amiss with your modem/wireless router/gateway device. Is the speed issue with wired or wireless or both connections using this gateway device alone?
I think the Apple devices are not capable of supporting anywhere near 1gbps speeds, except when hardwired where applicable
Not just Apple. Also remember that the newest 802.11ac version of the AirPorts came out over five years ago and have not had any significant updates since.
If you want to compare router performance, I suggest that you take a journey over to the SmallNetBuilder site where they compare numerous devices.