Pensions are a right because we are all supposed to be paying into the pot anyway: it is simply a government run savings scheme. The difference between it and say housing is that it isn't to do with sorting out present issues but providing for the future.
If you want to change it to be a safety net for some only, then you create disadvantages.
Firstly you get those that are presently contributing to the government pension pot paying into a commercial pension pot instead (or at least those who make the effort to do so and who see it as a good thing to do when the safety net is there for tomorrow anyway) thus making some private individuals rich instead of ploughing all the collected money back into the system.
And also, as I imply, there will be a group that could save but who don't bother, preferring a spend now rather than invest for tomorrow philosophy, so the welfare spend may well will be greater. Not a desirable event.
In addition society will degrade into a less caring, more "sort yourself out I don't care much" one, which can't be a good thing.
As things stand those who can contribute do and those who can not are provided for anyway. Those who could and don't are always impossible to identify with 100% certainty so it's not worthwhile worrying about it.