That is the way many people do it, and I have not yet heard of a case
where someone has been nailed for it. however, the guy who will turn
you in for it is probably not the tower controller, but an inspector.

It would be interesting for you to contact your tower personnel and ask
them this question and see if you get the same answer.

But my interpretation was told to me by an FAA inspector, one of the
types who would indeed file on you for it. If that happens, it will
not matter that you have been doing it for years and the tower said
nothing. The FAA's position is that if the tower wanted you to enter
on base, downwind, crosswind, they would have said so. Enter left
traffic means, in the minds of those FAA inspectors I have spoken with,
to go out and get on the 45 and enter the pattern like anybody else.