They don't necessarily need to receive rent payments to 'clean' the money. It's possible that what is regarded as money laundering in their country of origin is not regarded as such in the country where they are buying the property.
This is empirically false. There is an incredible range in the price-rent ratio across different real estate markets - from 50 in Hong Kong to 5 in Detroit.
That holds for everything. Only if they necessarily also move in the same way does this have any meaning, else it's like saying two points connect to a line.
If you kill all the bears in Montana, or add a thousand more, the number of ants in Brazil doesn't change. They are not proportional, they're completely unrelated.
"having a constant ratio to another quantity"
Inversely proportional too is a mathematic relationship with specific meaning (for one the product must be a constant). It doesn't just mean "more pesticide, less ants" (that's a more general statement than inversely proportional).
Perhaps you merely meant correlated with respect to the rent. But even so, in this thread there were so many provisos added, that the relationship is nebulous at least.
If all else isn't equal, i.e. you change interest rates or tax rates, then you're changing the constant. But they're still proportional with the new constant. You're only changing the ratio, not the nature of the relationship.
https://data.oecd.org/price/housing-prices.htm
Check e.g. historical data (untick "Compare variables") for "Price to rent ratio" for "United Kingdom" from 1990 to 2018.
> Rents are essentially always proportional to real estate prices.
which is demonstrably not true in any way shape or form.
See e.g. [0] pages 13 and 15 (pages 15 and 17 of pdf) for "median house prices by London borough" and "median monthly private rents by London borough". Westminster has higher rents but lower prices than Kensington. So, yeah, sure, if you include "desirability" in your variables, then you can probably get a regression fit but then the argument "rents are proportional to prices" no longer really makes sense (i.e. you're taking the proportion to be a proxy for desirability and then adding it back to the regression).
[0] https://www.london.gov.uk/sites/default/files/house-prices-i...
Changing other components of real estate costs doesn't destroy the proportionality with prices, it only changes the ratio. The same is true of property tax -- raise the tax rate and sale prices decline while rents increase, because rents are also proportional to every other component of overall housing costs, not just the initial principal amount.
It's like saying retail prices aren't proportional to wholesale prices because if you raise commercial rents then the ratio changes. They're still proportional. If you raise rents then retail prices may increase because the retailer has higher costs. If you then raise wholesale prices, the retail prices don't stay the same just because they've already increased, they increase even more.
Meanwhile the way a normal market responds to high rents is by building more rental properties, because when rents are high doing so is profitable. But that requires buying existing land and constructing new housing on it. If the existing land is owned by people who are neither developing it further nor selling it, that can't happen.
Which is particularly problematic in places with restrictive zoning, because they could be sitting on the specific properties that are zoned for higher density than what they're currently built to -- and those are exactly the properties you would want to buy if you were an oligarch speculating on real estate.