"People do not decide to become extraordinary....

[Lord Gothmog]

I am not sure it makes him less of a hero - at least not in my eyes.

Nor it would seem in the eyes of Tolkien.

From the ever-quoted letter 131 to Milton Waldman.

I think the simple 'rustic' love of Sam and his Rosie (nowhere elaborated) is absolutely essential to the study of his (the chief hero's) character, and to the theme of the relation of ordinary life (breathing, eating, working, begetting) and quests, sacrifice, causes, and the 'longing for Elves', and sheer beauty.

In the case of Aragorn and others of similar stature, they did have a motivation to "decide to accomplish extraordinary things." This could be seen as being "Born to a high destiny", or simply wanting to "Live up to the stories of their forefathers". But in the case of Frodo he was thrust into the role of a "Hero" by accident while Sam ignored all other things in his life for the simple task of 'helping his Beloved Master' (I use the term Master in the same way that it is done in the book, that of employer and Master of the House.) In so doing, he became a greater hero.