What speed and distance is the AC1200 mesh capable of? I have 1Gig coming into my home. Right next to the first point, same room, I'm getting 500Meg. (Nothing else on-line.) Next to the second point, second floor, I'm getting only 300Meg. And one room away from the second point I'm only getting 60Meg. Next to the third point, third floor, I get 45Meg; and across the same room I only get 30 Meg.
AC1200 2x2 means – at most – two streams of 433Mbps each in the 5GHz band, for a maximum of 866Mbps. But, that assumes you're in the same room and right next to the access point and using a client that has support for at least two streams. It's also before taking into account the fairly substantial overhead in WiFi. 500Mbps is not unreasonable for something like a phone, tablet, or even most laptops. So, I am not surprised at that result.
Next, we need to cover how the secondary points talk to the primary. They use a hidden WiFi network running an 802.11s mesh to talk to the primary (and each other, if required). But, this network is using the same 5GHz radio as the units are using to talk to nearby 5GHz clients. So, any 5GHz traffic through a secondary is going through that secondary's 5GHz radio twice, and using the same 5GHz channel twice. So, the available throughput will be lower. That client might be talking to the nearby secondary at the maximum speed, but the secondary definitely isn't going to be talking to the primary at the 866Mbps rate, since it's a room or two away through floors and walls. I'm actually impressed you managed 300Mbps through a secondary at that distance, to be honest.
The 60Mbps number is a little surprising, but as you move further away from the secondary, the client will have to talk to that secondary at a slower speed (and as we discussed above, the secondary is talking to the primary at a slower speed already). Still, I'd open up the Google Home app and check the details for that client to make sure it's connected to the secondary you think it is. If it's an Android phone (from certain manufacturers), it might not be handing off between access points, but if it's an iPhone, it really should do a good job of that, though you need to give it 30 - 60 seconds to initiate a hand-off.
As for the third point, I would say you may be running into an attribute of the mesh network. The path selection algorithm prefers fewer hops, so if that third point can get through directly to the primary, it will do so rather than going through the one on the second floor. Since there's only one 5GHz channel, this is often better than adding extra hops. This is why the placement advice for optimal performance is to put the primary as close to the center of the home as possible and then place each secondary no more than one or two rooms away from the primary – close enough to get a strong 5GHz mesh connection. From there, the secondaries will provide both 2.4GHz and 5GHz coverage to more distant clients.
I know this all sounds complicated, and under the covers, it definitely is. But, with optimal placement, you should be able to get reliable coverage over a larger part of your home with a mesh system than you could with a single traditional access point. WiFi is a convenience technology, though – you're not going to be able to saturate a 1Gbps internet connection through an AC1200 system. But, the primary does have a 1Gbps LAN Ethernet port you can use to build out a wired network in your home, and that network will be able to saturate your internet connection. Running as much of your bandwidth-intensive traffic over this Ethernet network (e.g., streaming TV, downloads, gaming) will then preserve as much of your WiFi capacity as possible for those devices that can't be wired.
If you really want to optimize your WiFi network as well, it's possible to connect the secondary points (assuming these are Google WiFi) to that wired network. This would allow you to place the primary and secondaries anywhere you want, since they will be talking to each other through Ethernet instead of the 5GHz mesh interconnect. At that point, performance should be the same for clients near any of them. I've done this in my home, since my cable modem is in the basement. I have a wired secondary on the ground floor and another wired secondary on the second floor.
I guess the summary here is that if you really care about performance, you may need to experiment with placement in light of the information above – perhaps even going as far as running some Ethernet cables.
I guess a follow up would be; is there a better system that I should be looking at in lieu of the Google AC1200 (to get higher speeds)?
Also, I was just told today that the Google mesh system does Not interface well with the AT&T fiber Gateway, which is my provider. Do you have any information on that?
A second thought is possibly to run an ethernet cable to the second floor for the first mesh point. Place two mesh points on the second floor and one on the third. Does that sound reasonable?
I'm using my phone so apologies for brevity. There are very, very few clients that can use more than two streams. Mostly higher end laptops. Phones and tablets are typically only two streams, and a lot of devices are only one. Point being, a WiFi system that supports more than two streams likely wouldn't provide measurably better performance for the vast majority of clients. I'm afraid I can't advise on other options though since I haven't researched anything.
I have heard some ATT customers have had issues, but I don't know whether that's more prevalent for Google WiFi or Nest WiFi.
Running Ethernet to wire secondary Google WiFi access points works really well. It's what I do and I'm very happy with it. Just note that if you do that, you'll want to wire both secondaries. A wired secondary can't act like an intermediary for a more distant wireless secondary.
Edit to add: it looks like you were proposing to move your primary to a more central location with one Ethernet cable. That's a good idea for sure. Placing the secondaries around it then will help.