I have tried to explain the sense of "good investment" that is meant by policymakers and voters and the cliche above. You have tried to explain that there is another sensible definition available. I don't disagree, but I think it is beside the point.
I feel like it is the point. The claim being made is incorrect.
If you have to invest a significant amount of capital to own housing and it isn't a good investment then people won't want to do it. But there are reasons we want to encourage home ownership, so if it actually wasn't a good investment then that would be bad. People would stop doing it. So it's important that the claim actually is incorrect; it can still be a good investment even if the value never goes up, because it avoids you needing to pay rent. If keeping the values flat would result in lower home ownership then doing that might actually be a problem, but it isn't.
The real problem -- the thing people actually care about -- isn't that the value has to go up. It's that they don't want the value to go down. If they paid $500,000 for something which is only worth $100,000 they're going to be pissed. But that's also what needs to happen, hence the impasse.
Why do we want people to buy houses? It incurs transaction costs and makes it difficult for people to relocate to be near their jobs and such. It seems like we should optimize solely for the cost of meeting people's needs - either by paying rent or by owning - compared to the sale value of their labor.
Renting contains a lot of inefficiencies. If you don't like your bathroom faucet and you own your home, you go to Home Depot and buy a new faucet. If you rent, that's not yours to change and now you have to negotiate with the landlord or live with it. Also, you might not want to put money into a building you don't own, but the landlord wouldn't want to put money into a building they don't live in. There are a lot of perverse incentives and transaction costs.
That doesn't mean renting should be prohibited -- if you'll only be somewhere temporarily or you can't afford to buy then you still need somewhere to live -- but in general it's something we'd want policies not to encourage.