Here's my tuppeny'orth of contribution to the debate.
I start with the caveat that the main negative factor for parents not being allowed into the country is emotional. An influx of older people into the country is a visible change to the population and culture of the country. While a significant number of young people can be justified on the grounds of a skills shortage, an influx of older people purely on the grounds of family reunion would not go down so well. Just to point out the obvious, most Eastern Europeans who are coming to the UK are of working age and contribute to the economy far more than parents of non-EEA migrants. Yet, their visible presence has led to the rise of UKIP.
Having dealt with a very important caveat, let's look at the practical reasons for not allowing non-EEA parents into the UK. The main reason that I can think of is not based on economy, but society.
Social Integration: Older people tend to adapt less to the British way of life than younger people. That is not to say that they can't, it is just less likely. They are more likely to hold on to what is acceptable in their home countries rather than in the UK. And what is acceptable back there may not be in the UK. What is more, that can have an effect on their grandchildren, which may interfere with their integration into British social mores.
It took the UK a couple of decades to accept and integrate with the influx of East African Asians in the 1970s and I have a feeling that they are not in a hurry to repeat the situation.
Insignificant economic benefit of savings: Except in a small number of developed countries, older people almost everywhere else will not have built up a significant enough investment for their old age (in £ terms). Thus, although their savings may be large enough in terms of their home countries, in UK terms, it is a pittance. It could be argued that their UK families would take care of them. However, that assumes that their children will always have the ability to do so, which is never possible to forecast. If anything were to happen to the family, the state may be forced to intervene. If there were a high number of people who fell onto state aid, that may have an effect elsewhere in the national budget.
Impact on local jobs: It is quite common on threads in these forums to request for help in getting family here to look after a wife during pregnancy, their grandchildren, etc. While that is quite common in the cultures that they come from, that takes jobs away from local child care centers, midwives, etc. So there is a perceptible negative impact, albeit small, on the local jobs economy.
If the parents have a few years of working life left in them, even worse!!! They are competing for jobs with the locals, hardly something that they would appreciate.
Outflow of money from the UK: I think that the notion of money and skills flooding out of the UK is a bogeyman. I'm sure the government would have looked at the scale of the issue, if it were to be such a major issue.
To begin with, if you have become a British citizen, a major part of your estate is likely to be in the UK, where it is going to be taxed. So no harm there.
Secondly, a lot of non-migrant native Brits go on holiday to South-East Asia and regions outside the EU. Conversely, London is one of the most popular tourist destinations in the world. Some of them may even be parents flying in for a visit. Such things, like karma, balance out.
I'll end my observation by saying that, with great respect to the OP, the question itself is flawed. The decision not to allow parents of migrants into the country was taken by a democratically elected government. When people vote, many people decide to vote based on their feelings. An influx of migrants, be they East European or parents of migrants, creates hostility towards migrants. At the ballot box, they will therefore vote for anti-immigration parties.
Therefore the question as to the practical impact is irrelevant. The question should be how to make it emotionally palatable to the public of this country.
PS: A tuppence buys a lot of thoughts from me
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