On the whole I agree with most of those who ask why anyone would specifically search for links to "famous" people - why on earth bother?
But I do get rather worried that some people to accept and adopt these runcible trees "linking" rather improbably back over centuries taking in almost everyone who was "Famous" along the way. As others have pointed out, usually it's quite easy to poke holes right through them if you look properly.
We all probably are linked to various famous names - but we just don't have accurate, documented records that "prove" it. So who cares? We get a load of interest out of managing to put each little person into their place in the jigsaw - and I'm proud of all my farmers, painters and decorators, silk weavers and dairymen, amongst all the others.
In fact I feel rather a perverse pride that with two lines traced as far back as is practical, to the start of Parish Registers, I haven't a title or a famous person ANYWHERE!!
Original poster, stop hunting the famous. If they're there, you'll find them in time. Hunt the ancestors and relatives, and you'll become fascinated by the lives you find, and forget all about fame.