Except is £1.50 per day - not each time you take your bike in or out.
So does charging for gyms make no snese? Or charging for swimming pools? Both of these provide benefits to wider society as well as the individual.
I think you're cranking up the rhetoric without understanding the context here. We're talking about cycle parking in London. The research shows that the overwhelming majority of cyclists in London are not the poorest of the population - in fact they tend to be amongst the better off.
And it is the bikes being ridden by this group of people who are most at risk of being stolen, as they have a resale value and London bike thieves are quite discerning. On the whole, London cyclists can afford to pay £1.50 a day for parking and many would happily do so - which is why such schemes are so popular.
We charge for car parking - including for hybrids. If your criteria are used, then why shouldn't low emmission car drivers argue that they should get free secure parking?
Not everything can be free. We have other priorities, such as education, health services, the elderly and the homeless, which have a far more legitimate demand on the public purse than cyclists.
The gym comparison doesn't hold much weight. Gyms are luxuries and commuting to work is a necessity. Why should safe cycle storage be a 'luxury'? It should be a basic right, the police and council are supposed to be there to prevent you being a victim of theft. Yes there is a certain amount of personal responsibility in this but whereever possible (And let's be honest this is possible here) you shouldn't be penalised for being responsible.
I take your point about there being more weathy commuters in london than your average UK city but if a city as wealthy as London can't provide free secure bike storage, what hope is there for poorer cities and again what sort of signal does it send out?
Perhaps we should just agree to disagree on a lot of this. However means testing might be a reasonable compromise, as use of these storage facilities should be free to those on basic incomes, benefits etc. The trouble with that though is it tends to be quite unpopular with the general public who see that as unfair.
edit: in response to the bit about hybrids. Yes, parking should be free for people driving hybrids in London as the benefits to the planet are very clear in reductions in CO2 emissions. This is the typical response you will get from people who believe that people should pay for the amount of carbon they use.