Agree with your thought. If they want to go full blown ecosystem, they are there.
I still believe Google is not in the game for the sales number or grabbing user pools but they just keep honing on experience and software by data mining. All hardware are just pawn in the play as they prove time and time again by dropping great hardware projects.
They don't bother about customer care too hence my conclusion reached as they are not in the game for market dominance. Still in R&D mindset to grab all data and move on to next generation idea.
All tech companies are now in the same business, don't fool yourself.
Obviously there are differences and some are better than others for now but even Apple is incorporating ads and tracks users in the App store. Apple is selling more and more services beyond hardware because of recurring revenue streams.
Like Apple Google is changing and just now starting to realize that providing it's own hardware is better for their business model. They also have a vested interest in keeping people connected to their services which they can do better with their own hardware. They most likely will start supporting their hardware longer to keep users connected to their services.
It doesn't matter to Google if you use a Pixel Phone, watch, or tablet but if they provide the hardware they don't have to deal with competing services like Samsung. But you can be sure they are waking up to the fact that hardware makes a difference and if they can dominate the space they will make more money on the hardware and their services.
The difference with Google is that profit on the hardware alone is not their priority. They can cut margins more than anyone else because they know they will make up for it in the services.
If all hardware was just a pawn as you say and move on to the next generation then why would they start making their own Tensor chips? It would be a lot easier and cheaper to just slap a mediatek chip in there and call it a day but maybe they want to improve user experience and be able to deploy a chip to multiple devices? Only reason to do that is to make better hardware.
I agree Google has a long history of abandoning projects but so does Microsoft. I think they are getting serious and hopefully will reverse the trend they have set too many times.