I used to do it in the days when I fished on the Dorset Stour, Hampshire Avon and a few local lakes.
I'd take a single rod with different tips - an "Avon" style rod is ideal - strapped to the top tube, and the rest of the tackle in my panniers and in a bag strapped to my rear carrier.
Sure, you're limited to what you can take, but it really is possible to enjoy a day's fishing without carry huge cartloads of tackle around with you.
On the subject of telescopic rods, a lot of them are really poor. I'm sure there are good ones out there, but be very careful if you go that route - it's no good selecting tackle for ease of carrying if it's poor for the job.
Alan