A rather quick survey. . . .

It has been said that Basil Rathbone loathed the fact that he was primarily known as the actor who played Sherlock Holmes to the greater public. Disappointed that some of his better works were not the reason he was best remembered.
We, as Sherlockians, know of Basil Rathbone's other works, as I am sure do most film historians.
But probably not the general public, if they know him, now, at all.

I did a quick check, using the list on wikipedia, to see how many actors who have played Sherlock Holmes over the years, were introduced as 'being best known as playing Sherlock Holmes' or some wording close to that, within the first one or two introductory paragraphs.

It is surprising, out of that list of well over fifty, how few actors are first introduced as 'being best known as playing Sherlock Holmes.'

Of the rest, many are great actors who are known for other rolls.
Others are actors not all that well known for anything memorable.

Now the question I have is: As an actor, would you want that to be your claim to fame, 'the actor best known for playing Sherlock Holmes'? Is that how you want to best be remembered? Or is it something you come to accept?
Does being remembered as such usually mean your performance as Holmes is accepted as an accurate or note worthy adaptation of the original?

Most of the ones that do share that claim to fame are ones that are still discussed as some of the best Sherlock Holmes portrayals seen on film.

Interestingly, at least for me, of all the actors, the only one I really have any knowledge of other notable film rolls happens to be Rathbone. All the others on the list I would have to research their other rolls.

Here is the ones I was able to pick out as being introduce as 'an actor now known best for his portrayal of Sherlock Holmes'. The list was done quickly, so may not be totally complete, but I think it is fairly close.

Jeremy Brett - not publicly known for other major film works
Nicholas Rowe - not publicly know for other major film works
Douglas Wilmer - in the 50's and 60's known for other works perhaps, but remembered as Holmes
Arthur Wontner - not known for other works
William Gillette - to long ago for most to know him for anything else (but was a major contributor to the world of Sherlock Holmes on stage and film.)
Ellie Norwood - again, maybe to long ago, but now best known as Holmes
Hugo Flink - Austrian actor known as one of the earliest actors to play Sherlock Holmes
Basil Rathbone -

Vasily Livanov - it is noted that his greatest success came at playing Holmes, but he is not introduced, yet, that way.

I have only hard that Nigel Bruce never regretted his association with one of Doyle's characters, but I have never heard of a Holmes actor that felt the same way. Although I get the feeling Douglas Wilmer may feel that way now. But did he as a younger actor.
Rathbone seemed to embrace the association later in life. But I get the feeling it felt like a burden for many years.

I don't think it will happen with the three current actors portraying Sherlock Holmes. Is that because their other work is better than their Holmes work?  Or is because their Holmes aren't that good?