I've been through this issue .. I hope the following is little helpful.
I have broad shoulders and a meaty chest. In the past, I carried much more muscle, but I've been 5'10", 170lbs for a while now. In any case, I come from a sports background where weightlifting is almost a must (ice hockey). In evaluating whether I should forego training and other sports in lieu of cycling focused training, I decided that I'm unwilling to give up weights and other sports, despite having a summer full of respectable and solid cycling efforts and extended riding time. It doesn't mean I don't love cycling and I don't ride hard, I just decided not to become focused solely on the bike.
I can tell you from my experience: if you like to lift weights, don't disillusion yourself with becoming part of the elite levels of cycling. My opinion is that, for 99.9% of us, cycling should be part of a series of various athletic endeavors. Cycling focused training means, when you train, you cycle! Period!
In terms of daily activities and sports, most of us gym rats (or even former gym rats) have other preconceived notions in terms of how we define strength and overall physical health. Maybe my experience was different from others, but when I was cycling focused, I felt weak at just about every other type of activity. Even though I was getting stronger and stronger for the riding time, I felt noticeably and generally weaker at tennis, running, weight training, skateboarding, etc.
As described above, I play a variety of other sports- and although my cycling power dramatically increased, I felt weaker in every single activity besides cycling. Even running a simple fast paced mile had me longing for a 50 mile bike ride instead.
So I guess this long winded post is the cliche of "be careful what you wish for ..." If you long to become a super cycling engine, be prepared to abandon your ideals about overall strength and athletic dexterity and performance in exchange for the uniquely tuned attributes of endurance athletes.