They could if countries let them... but airlines would get fined AFAIK. I mean that is what seemed so farcical about Merkel and her "refugees welcome" nonsense - it isn't like she allowed them to just pay for a plane fare - instead they had to run a gauntlet through a bunch of other countries to get there and pay far more than the cost of a plane ticket to people smuggling gangs. Also meant that the people who were able to be "welcomed" in Germany and the rest of Europe were disproportionately the people who were least at risk in the first place - mostly fit, military aged young men. Of course a relative lack of women caused some obvious problems there too.
There was that really sad story too of the little toddler being washed up on the beach - though, counterintuitively, it was seemingly used by people in support of the policy that lead to his death in the first place... the family the little guy was from were already safely in Turkey, living in a house there but decided to chance it along with all the others following Merkel's call.
But no, they won't let them buy plane tickets (or indeed provide them for people who can't) - they've got to risk it all in unsafe boats/dinghies themselves.