"Social homogeneity" is how you get suburban shitholes in Utah where the police trip over themselves to defend a LEGO pawn shop owner from being served papers. People blamed the "Mormon Mafia[0]" for that, but the real problem is just that social homogeneity
sucks, especially if you're on the receiving end of it.
As for population decline, I will give you that all the people who are currently very loud-mouthed about it are also far-right grifters who think The Handmaid's Tale is an instruction manual and want to turn America back into a shithole slave-breeding colony. The underlying concern is basically "I won't have enough cheaply-hired peons if people don't breed like rats". But, notably, all those people are also anti-immigration and basically want every country to be a closed off ethnostate breeding compound.
Anyway, migration is a human right.
What do we mean when we call something a "human right"? Well, usually, it's to mark some activity as sacred and untouchable. Like, when we say free speech is a human right, we're saying that speech is untouchable by law. But there's a deeper understanding embedded in this: humanity has been doing this activity freely since before we could remember, therefore anyone trying to restrict it deserves scrutiny.
For speech, we have documented evidence of people treating speech as a human right for hundreds, if not thousands of years. But the history of human migration goes back orders of magnitude further. A constant of human civilization is that when people don't like what is happening, they leave. Humanity's motto is "If it sucks, hit the bricks"!
So personally, I don't see this as a case of "people are abusing poor Japan's visa programs", but a case of "you built a dumb system of selling visas for money and were surprised that people figured out how to cough up the cash". Of course that was going to happen. People are going to bend over backwards to comply with your visa requirements no matter how stupid the visas are, because, again, migration is a human right.
Hell, I doubt Elon Musk is going to argue he should be sent back to South Africa. The rich racists don't even think the racism should equally apply to them.
But sure, yes, "cultural preservation" is important. Let us not ask too closely what that culture is, or if it's worth preserving[1]. Or even if it is being preserved. Because in the specific case of Japan, the population decline is primarily happening in remote rural towns. That culture is dying, today, because they are running out of people. Would having foreigners move in change that culture? Sure. But culture changes all the time! Trying to preserve a culture by sealing it off from foreigners is like trying to preserve a river by sealing off the water flowing through it!
[0] American Fork is something like 90% LDS members. If you go a little more north to anywhere in Salt Lake County, it's more like 50%. And my personal experience as a church member is that American Fork members do not recognize anyone from out-of-town as a member, even if they are.
[1] Likewise, the Japanese countryside has its own small town dynamics that are equally as shitty as American Fork, Utah. Go look up the story of Rin Japanese Country Life if you're curious.