Many (possibly most) people don't find out that they've been named as the executor of a will until the testator dies. There's no requirement for the testator to tell anyone who he has named as executors.
When I was MD of a will-drafting company, one of the things I constantly stressed to clients was that it was essential for the testator to let other people know where his will was kept. He might choose to tell the executors, or the beneficiaries or someone else but it's essential to tell somebody. (I'm sure that thousands of wills are ignored, upon the death of testator, every year - simply because nobody even knows that a will exists, yet alone where it is).
Unless the solicitor is named as an executor, it's now unusual to leave a will with a solicitor. It would be better for the testator to keep it with his private papers or leave it with an executor. (Even if a solicitor is named as executor, I'd advise against leaving it with a one-man legal practice. Long before I worked in the will-drafting business, I had my will drawn up by a solicitor and left it with him. He's since retired and died, and nobody knows what's happened to the wills that were in his care. I've since revoked that will, so it doesn't matter to me but it might cause a lot of problems for other people).
Chris
(PS: Both of the executors of my will have unsealed copies of it, together with a written statement of where the original is kept)