To be totally honest... I think a frame pump would look great with one of my vintage bikes. But I try to keep my modern daily rider sleek and clean looking. I only added the 2nd water bottle for the heat wave.

The tube, inflator, one cartridge, a couple tire levers, and tools... is all I can cram into my saddle bag. And I always have my phone!

I did have a flat reasonably far from home once.... and made a two mile or so detour to a LBS for a new spare tube and CO2 cartridge.