Because when a term is in such common usage for that length of time, getting hung up over semantics and the use of the word socialist vs socialized is counter-productive. I would bet that if you were to review Ronald Reagan's speeches on the issue of private versus nationalized medical insurance you would find he used the term "socialized medicine" to refer to the idea of national/socialist health care for the simple reason that it was the conventional, established, common usage term for such a program.
Yes, you’re correct, Reagan did use the term “socialized medicine”.
And for the sake of accuracy, in this 1961 speech, he opened by equating “socialized medicine” to socialism, and continued to the end with that theme:
Now back in 1927 an American socialist, Norman Thomas, six times candidate for president on the Socialist Party ticket, said the American people would never vote for socialism. But he said under the name of liberalism the American people would adopt every fragment of the socialist program....
{snip]
One of the traditional methods of imposing statism or socialism on a people has been by way of medicine.
[snip]
Now let us see what the socialist themselves have to say about it.
{snip]
From here it is a short step to all the rest of socialism.