Yeah, this sounds like a classic from the “total bullshit L1 tech support will say with absolute confidence” files.
There is an outside possibility that there is some specific config setting on their bundled router that they don’t tell you about which causes traffic shaping to get applied to your connection if it’s not present, but that would be insane and illogical. If the new ISP-issued router actually improves your performance, that’ll probably be why. But like you, I bet it won’t.
I have used Ubiquiti for my home network for years, and it has always worked great at what it promised to do for me. People’s frustrations with it—in my experience—usually revolve around things they want it to do that it doesn’t, and the fact that it is very unfriendly to hacks or jury-rigging. So you have to be very sure going in that it matches your requirements. It’s like Apple gear.
Another option you could look at is TP-Link’s Omada system, which is basically their clone of Unifi but has a wider variety of hardware options.
I also often see people using Ubiquiti switches and APs in combination with a pfSense firewall if they want more sophistication and configurability. If you’re coming from Sophos and want to do sophisticated routing and filtering, you’ll probably find the Unifi firewall lacking in features (but it works great for people who don’t want to do that).