Although the easiest route (no-fault eviction) is being abolished soon, wanting to sell a property remains a valid reason to evict.
Some people just buy property as a speculative investment.
I do not think it is the main cause of shortages in London - that is people buying holiday homes, which are often large and centrally located. London provides a lot (restaurants, nightclubs, gambling, prostitution, financial services...) that attracts people with a lot of money to spend from all over the world.
"Easy" is relative. "Evicting" an airbnb'er once the term is up will always be orders of magnitude easier than kicking out a long-term tenant who regards that as their actual home. There's not even anything necessarily wrong with this! The easiest way to address the issue is literally to slash any remaining red-tape that's making things difficult for those who would want to AirBnb these properties out, while managing the resulting side-effects (including the plausible effect on the long-term rentals market) by levying a special fee if necessary.
As a bonus, easy AirBnb rental provides an alternative for some who might otherwise want a permanent holiday home.