Using retirees as a tool to work against property taxes has historically been an effective strategy, but it's important to remember:

1. What we're actually trying to accomplish
2. Will the proposed change be effective in accomplishing the goal
3. Will the change have other consequences that are negative to the extent where the potential benefits outweigh the consequences in aggregate
4. Are there any alternative means to accomplish the original goal

One-by-one:

What we're actually trying to accomplish

Seems to me that the root question is one of housing affordability, in particular for retirees, who may have a lot of assets, but limited cash flow

Will the proposed change be effective in accomplishing the goal

Reducing/capping property taxes does indeed make it easier for some retirees to keep affording their homes, but reducing property taxes makes real estate a more lucrative investment, driving up the overall prices of real estate. This applies for both private persons intending to use the property to live in, for private persons looking seek rent, and corporate actors doing the same. Messing with property taxes is a large part of the housing affordability issue present in many places in the U.S and elsewhere (zoning laws being another major contributor, in particular those mandating single family homes, and lack of public housing being the other major contributor). Hence, this change would only benefit those lucky enough to have purchased a home in the past, at the expense of all retirees not already that lucky, which are now less likely to be able to do so.

Will the change have other consequences that are negative to the extent where the potential benefits outweigh the consequences in aggregate

Apart from driving up the prices of real estate for other retirees, everyone else interested in purchasing a home will also feel this broad increase in prices. This has led to large swaths of the population being effectively priced out of home ownership. This has the second order effect of making owning rentals more lucrative, as higher rents can be charged, further exacerbating the larger problem of housing affordability, but now also for even poorer people.

Finally, reductions in real estate taxes limit what public services can be funded through their use. In the U.S, this primarily means schools, infrastructure, firefighting, transit etc, all of which are suffering a lot in quality, much as a consequence of having messed with property taxes in the past.

There's a very, very strong case to be made that the consequences have very much outweighed the benefits in this scenario. I would even say that they have been devastating, being part of the root cause of a large amount of issues seen today.

Are there any alternative means to accomplish the original goal

There clearly are good means to tackle this problem in other ways, the principal of which I believe should be massive public investment in social housing. By building a huge supply of high quality homes affordable to everyone, we make sure no one will have to be forced to go without an acceptable home, regardless of whether they are retired or not.

The second strategy should be to entirely remove the kind of zoning laws that have contributed to the kind of increase in housing prices seen today - mandating that only single family homes should be allowed to be built on massive lots with low utilization is hugely harmful to housing affordability.

These two measures would address housing prices having gone up in the way they have historically, which would also lead to property taxes not rising in such a dramatic fashion.

What should never be done, however, is reducing or capping property taxes.