Sorry - nice idea, but we're not communists.
They are making millions of pounds of profit a year, enough to pay for the complete training of new pilots from scratch, yet alone type ratings.
All very true, but disgregards the fact that it is someone else's money that is invested in the capital of the company, which requires a profitable return for them to continue to invest in the company. With even BA earning less than a 10% operating margin, the investors are getting little for their money compared to putting it instead in other industries or even in other markets.
Eating into this to an extent that is unreasonable means the whole operation may be returning less than the investors require, and make holding their money as cash more appropriate.
The fact that a profit exists does not make it available for use by stakeholders other than the shareholders.
The fact that the job market operates the way it does is symtomatic of what people are prepared to do. Without you being a dictator and taking over the job market, and indeed all other power in the country, you will never be able to impose the model you propose on people who have freedom of action to do as they will...and if you impose it upon them, they will revolt.
Bottom line is - too many people want it, and even after massive growth in the industry, there are insufficient spaces for all.
The only simple answer is to impose selection based upon potential and innate ability prior to starting flying training. Sod the idea of the 1000hr flying instructor deserving a place first in the line - in a large number of cases, there is a very, very good reason why the airline will NOT hire some of these individuals!