It is better to carry too much kit rather than too little, just like it is on the fells
If you use good tyres, which you most definitely do
, and pump them up to recommended pressures (the rear is likely to be more than the front) and inspect for cuts, stone damage and flat spots regularly (ideally before every ride), then you will very rarely puncture if you stay on the tarmac.
I have vivid memories of changing an inner-tube in a bus shelter in Wirksworth, (it was a Sunday I should point out), sheltered from the piddling rain, and I've lost count of the number I have changed by the side of the road (club cycling in a group etiquette is that you
must change the inner-tube).
Only last year I encountered a man standing by his bike, which was on its back with the rear wheel missing, a third of a mile from the Coventry canal. I offered my services, as good etiquette demands, and to my disappointment he said he
did require my help.
He couldn't get the tyre off with his tyre levers. There was nothing wrong with the levers, he just lacked the technique, so I took the tyre off showing him how to do it in the process. I then threw the punctured tube onto the verge and said
"Have you got a spare inner-tube?"
"No" he replied.
I gasped at this, as I was having difficulty in not calling him a flaming idiot (or a lot worse).
"So how are you going to fix it?" I asked
"I've got a puncture repair kit" he said, proudly.
At this point I said I would have to leave him. For those of you who think I am a heartless so and so, I should point out we were 100m from working earth-moving equipment at the HS2 site, 200m from the West Coast mainline railway, 400m from the raised A38 (one of the busiest non-motorways in the country), there were cows the other side of the hedge, regular car traffic on the lane, and there was a gentle breeze coming across the flat plain. The chances of finding a puncture, without water, in such a location were virtually zero, so I suggested he explore the field of cows for a water trough.
The moral of this sad story is that if you do carry tyre levers, make sure you carry a spare inner-tube as well