Your cousin, also a beneficiary, can reply with a no to the solicitor. The solicitor will inform the executor that two beneficiaries have declined to agree to sell the house to him because of the cousins offer.
The executor, whose role is to get the best value for the assets, and who looks like is not trying to do anything underhand will consult with the solicitor and propose another solution. It might be handy if the beneficiaries had a quick meet up to discuss, it would certainly be faster. But I can see why the solicitor would write to everyone to get their individual yeah or nay as some people may not feel they can give an open opinion in a meeting. It is just slow, the solicitor is juggling a lot of files at the same time so cannot react instantly to one executor.