An interesting question.
In part the answer is, simple tradition. Once it has been established that the sonnet is the form for a love poem, great poet/lovers later worked in that tradition because it was expected of them.
However, there are three formal reasons why it is a great form for love poetry. The first is also simple: it is short enough to read quickly, but long enough to really develop an idea.
The second is more complicated: like love, there is variation within established form. By that I mean, just as your first date and my first date might be different, but they both share certain qualities, so the known structure of the sonnet creates a pleasant expectation: how will this known stage be navigated?
Third, the larger structure of the sonnet, whether 3 quatrains and a couplet or 8 and 6, creates a good progression. One can either work through three elements of a theme and then wrap it up, or use a call and response structure (problem and solution, question and answer), and love involves questions that get answered the way you hope for them to be.