Yes , people riding with a frame pump or a mini frame pump will use this in conjunction with a repair-kit (spare tube, patch kit, tire levers).
Most if not all recreational cyclists carry some method of a repair kit because flats happen and it doesn't have to mean the end of your ride.
Generally with practice a reasonable time to fix a flat is 5 minutes.
Those 5 minutes spent fixing a flat will be much faster than calling an Uber or your SO for a ride, or even resorting to public transit.
Better yet spend those five minutes changing a flat and then go finish your ride!
You don't need a lot of bike tools—you, just need the right tools.
A frame pump is one of those tools...
A frame pump can be seen as a one time cost to get air into a deflated tire.
Whereas others use a CO 2 cartridge to inflate a tire, but over time a few bucks for one cartridge adds up.
A pump and a CO 2 cartridge have their advantages and disadvantages, but in the end the result is the same—fix a flat and be on your merry way!
Some satire on the matter can be found here .
bicycles.stackexchange.com/users/29093/Nikolai
Generally, most prepared cyclists carry a spare tube, some tire levers and a bit of money or something else that could be used as a tire boot.
With these, if you have a damaged tire or tube, you can normally put in a new tube and continue your journey.
For tubeless riders, a spare tube is sometimes necessary.
A pump or CO2 cartridge is necessary to inflate the tire.
CO2 is nice because its quick, and you can reseat a tubeless tire if necessary with one, but it is wasteful and once you're out of cartridges, you have to go to a pump anyway.
I carry both, just cause a small pump can be tiring on your arms.
A patch kit is useful but usually you end up replacing the tube on the road and patching it at home so that the patch is reliable.
Another use of a frame pump is to get dogs to go away .
In any case, I leave mine on my bike normally so its always there (its a mini, and attaches to the underside of my rack, so nobody sees it).
If I'm riding around town, I won't carry a spare tube or levers since its less of a hassle just to walk the bike home or catch a bus, but when I go out of town, I carry them just cause there aren't many options to get home without fixing the flat myself.
bicycles.stackexchange.com/users/8219/Batman
I use (tough) touring tires.
If I have a puncture it's usually a slow one, from a sharp piece of grit (embedded in the tire) that has finally managed to work a tiny pin-prick through the outer tire, and begin to hole the inner tube.
I've been able to get home after discovering a slow leak, simply by stopping to re-inflate every 40 minutes or so (and without even finding and removing the offending grit until after I get home).
I also now carry tire levers and a spare inner tube.
I don't count on repairing a puncture (hence the spare inner tube): to find a puncture when I'm at home, I need to submerge the faulty inner tube in clean water and look for bubbles.
bicycles.stackexchange.com/users/1097/ChrisW
Pumps have other uses as well.
If you have a tubeless setup, punctures can be sealed by your tubeless juice, but still cause some loss of pressure before self sealing.
In that case, carrying a pump without a patch/spare is completely appropriate.
It allows you to replace air lost while your tire sealed itself.
Additionally there are styles of riding to which frequent pressure changes are important.
Winter cycling races are a good example.
Over a long course , it may be well worth it to put additional air in your tires if trail conditions improve or the temperature drops significantly.
Punctures are of small enough concern during winter racing here that I often don't care a spare tube, but will still carry a pump to adapt tires to changing trail conditions.
bicycles.stackexchange.com/users/13710/Deleted User
I carry a spare tube, a pump, patches and glue.
Because if I get a flat tyre I don't want to be stuck pushing the bike.
Simple as that.
bicycles.stackexchange.com/users/25176/Kilisi
I've seen people fit tire/tyre pumps to their bikes. What's the use in that?  If I have a puncture it's  usually  a sizable hole in the tube, such as a piece of glass that pierced the tube.  I could image that the pump is for if you  also  carry a puncture repair kit, plus levers to get the tyre off. Is that the use in carrying the pump?
What's the specific use in carrying a pump?
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bicycles.stackexchange.com/questions/43456
bicycles.stackexchange.com/users/26820/edev
Generally, most prepared cyclists carry a spare tube, some tire levers and a bit of money or something else that could be used as a tire boot. Punctures happen and they have to be fixed, especially you are out of town and there is no other way home. The pump puts air into the flat tire.  Usually a pump is carried for use with a repair kit or spare tyre, but it can be used to pump up an underinflated tyre or slow flat without repairing the leak. A basic set of tools and spares is important to allow cyclists to continue after a puncture or other minor problem. CO2 cartridges and air pumps have advantages and disadvantages, but both will do the job.
Usually a pump is carried for use with a repair kit or spare tyre, but it can be used to pump up an underinflated tyre or slow flat without repairing the leak. A basic set of tools and spares is important to allow cyclists to continue after a puncture or other minor problem. CO2 cartridges and air pumps have advantages and disadvantages, but both will do the job.