[NEW ANSWER FOR REPHRASED QUESTION]
1) a) OK. So let's imagine opposite situation. Let's say that there is such nice district of identical houses. Shall we use their historical transaction prices? So one guy haggled more while buying, so should pay lower tax. His neighbour overpaid because he bought in the middle of housing bubble - he should pay much higher tax. Third one inherited from his parents. Shall we use the price that they paid many years ago, it would be much lower...
[Such idea would not only be rather unfair, but also would motivate not to move, as it would cause painful tax reassessment]
b) Inflation. Prices of everything went 3% up, salaries went 3% up. Gov needs 3% more money to keep public services on the same level. Sure, prices of everything would increase, except taxes on housing are supposed to be frozen, right?
c) "beyond the control". Yes. Taxes in general are not supposed to be punishment for misbehaviour, but a way in which society collectively finances some common goals. Moreover, the whole point is to tax possibly things that are beyond control - when countries were taxing real estate based on things being under control (like number of windows) people started enthusiastically bricking up windows.
2) a) Retirees are highly disciplined voter group
On the other poor are highly undisciplined voter group
In consequences, from political perspective it makes much more sense to cater the old and ignore the poor. That's what the nation want, as shown in perfectly democratic voting. Sort of...
b) If we provide old people with some tax cut, then more people would become old... Luckily not. ;) On the other hand there is an issue with poor. Such system, often lead to perverse incentives, as person who starts working hard some crappy job is losing all benefits and preferences for the poor. When multiple handouts and preferences are being granted in not well thought and coordinated way, then there is a risk that a hard working poor person would face an effective tax rate of over 100%. (and later we would call it as outraging moral problem when such person is trying to avoid a work that would actually cost him extra money... ;))
c) Technical issues. As we all know tax system is overly simplistic, and should be done in more sophisticated way, right? :D Who is a retiree is quite straight forward. Who is poor is not. How exactly to calculate it? Shall it be checked every year? Month? Shall the person lose such status if does not try to find a new job?
[/NEW ANSWER FOR REPHRASED QUESTION]
1) Maybe they are not so poor?
Well, the thing is that we already figured out that they have a nice real estate which value went up. If we skip emotional language "having a real estate of high value" does not sounds so much as typical feature of poor people, at least not in my country. Sure, exceptions happen, however aiming at taxing property (like real estate) would tend generally to target richer segment of society, so if one want want to target those pesky rich, he should rejoice tax on real estate.
2) Real estate taxes are hard to avoid or evade.
In contrast to something as esoteric and hard to pinpoint like income, existence of a structure made of brick and mortar is a bit less controversial and easier to prove. Buildings also have this nice property that they do not escape to low tax jurisdictions.
3) Capturing land rent by gov
Usually there is an issue that taxation discourages some activity. (think in line of any carbon tax, where its exactly the point) In case of real estate, their value and implicit land rent is often result of artificial scarcity caused by gov intervention called zoning law. In consequence real estate value goes up, its not being capture by some investor but by gov.
[Hint: next time try to write a question in less emotionally loaded way]