Great question ferdinanda and one I’ve pondered as well. I think your theory could be a valid one.
Another perspective on this would be that the Doom of Men as it was later referred to, or their mortality, was originally known as the Gift of Men. I believe it was known as a gift because the elves were bound to Arda, and due to the marring of the world by Melkor, their long lives would eventually leave the elves filled with sorrow (hence all the ‘grey is the shadow upon my heart’ stuff you hear from elves). From this perspective, it was considered a blessing or a gift to be released from Arda through death and to no longer carry these burdens.
Therefore, we can speculate that Elros wanted to labour for a while longer in Arda, and then be able to pass out of it. Immortality sounds great at first but I think that actually living that long in a fallen world would certainly take it’s toll and be much less glamorous after a few centuries.
"I do not love the bright sword for its sharpness, nor the arrow for its swiftness, nor the warrior for his glory. I love only that which they defend," Faramir in TTT by JRRT.