No wonder engineers bills are so high. Changing an inner tube does not require that much work on a Cessna in my humble experience. That kind of work gets done on my annuals.
Fortunately we have airworthiness standards which take your opinion completely out of the picture. Airworthy implies both legal and safe; without both, it's not airworthy.
One might as well suggest that going to dental school is a waste, and dentists charge too much. It's not time for the annual checkup, so go ahead and drill the tooth and do your own root canal or filling...have the dentist checkit at the annual checkup.
Then again, some of us underwent several years of training, and many more years of on the job experience, for something, one would hope.
It's not just a simple change, like a bicycle.
What I had in mind in my original post was this:
You're at an airfield with no maintenance facility, a long way from home.
Your tyre goes flat.
You have either a spare tube, a puncture repair kit, or a tin of tyre weld.
You also have access to any tools you need.
Your regular maintenance organisation can't come out to you for a week because they're too busy and it's too far.
You're very experienced in things mechanical.
Do you get the train home and wait for the licenced engineer to find time to get to the aircraft, or do you effect a repair and fly home or to an airfield where maintenance is available?
I know what I'd do!
By all means, tell us what you'd do. Apparently not do it right, at the very least.
I'm not sure what tire weld is, but presumably you're talking about a can of fix-a-flat or something along those lines. I'm not aware of "puncture kits" made for aircraft, so presumably you're talking about something you've come up with at the automotive store of a bicycle repair shop. Red flags should be flying already, but apparently you're comfortable with this, so let's move on...
Aside from the fact that you have no idea why the tire is flat...aircraft tires seldom go bad because there's a nail through the tire...you're talking about using unapproved and unsafe methods to effect the "repair." You're talking about taking a wild shot in the dark at the repair. Where a car or bicycle gets a puncture and leaks, aircraft wheel assemblies generally do not. There are usually two places that the leak will occur, neither of which are addressed by, or handled by a can of fix-a-flat or a bicycle repair kit.
Leaks generally take place in the wheel parting half (most commonly through the tube and then the wheel parting half if you've using a tube, and then most commonly because the assembly has been done incorrectly and a tube has been pinched), or in the valve stem. Often a leaky valve stem may be corrected by tapping the valve core, as this is the most common source for the leak. The valve is reseated, and a little spit on your finger can be used to assure that no more bubbles are coming from the valve...problem solved. In other cases, a simple adjustment with a valve stem tool will do the trick,when the valve stem core has backed out a little. Do it a little too tightly, however, especially on an older assembly or older tube,and you may have it comeflying back in your face. I've seen people nearly lose an eye that way.
Leaks from the wheel parting halves are taking place internally, with the leakage taking place through the axle area, past the wheel bearings. This is occasionally due to an improperly assembled wheel or an imperfect seal, but more likely due to damage. If it's damaged, then there is absolutely no excuse for failing to obtain a very thorough inspection of the wheel itself. You could very easily have a failure. I was director of maintenance for a corporate department some years ago that operated among other things a Sabreliner 60. Shortly after I left, my replacement failed to properly inspect a wheel assembly and it failed during a landing, destroying the aircraft. You may think it's okay, you're only in a 172...that little wheel assembly and that little tire are all that's separating your airplane from the ground...that little aluminum or magnesium fragile assembly. It's cracked and leaking, do NOT go fly. Wait for proper maintenance.
There is absolutely NO excuse for get-home-itis, that urge to get home at all costs, that leads one to excuse shoddy maintenance or quick-fixes in the interest of getting by in a pinch. Just don't do it. It's not legal, it's not safe. Justification is the narcotic of the soul; don't become an addict by trying to justify your way out of something you should not.
You may or may not be "very experienced in things mechanical." If you're talking about shooting a tube of fix-a-flat into your tire, then you're not that experienced, or you have very poor judgement. If you have all the tools in the world available to you, then what on earth are you doing proposing a scenario in which you cobble the repair together and go home?
When you shoot that can of fix-a-flat or tire weld or whatever you want to call it into that tire, severly unbalancing it and replacing the inert nitrogen atmosphere inside the tire with flammable gas, you also put the rubber compound in which gasses as the tire heats with use, further increasing the potential for a blowout or explosion (and don't bother bringing it to me for repairs after you've shot that junk into the tire...it's your problem now). You might as well trash the tire too.
So, you have a wheel assembly which may be damaged, you have know way of knowing, and you know what you'd do; you'd cobble it together and go fly because you don't want to wait. You have an unlimited supply of tools available, anything you need (calibrated torque wrenches, etc), but not a single mechanic in sight with whom to consult or get the job done properly? Interesting. Someone just happens to have a hangar full of the right equipment sitting open at this remote, abandoned airfield where you've gone? You've got a lot of luck on your side.
When you fly, you need to be prepared to drive home, wait for repairs, sit out weather, or even buy an airline ticket home; that happens. Don't go making excuses to get you on your way. I've heard them all. I ran into an individual years ago who threw a rod through his engine case on a Navajo, then wanted to put cardboard over the hole in the engine, fill it with oil, and fly it home. I kid you not. I've seen landing gear wired together, garden hose used to replace brake lines, parts held on with barbed wire. Each one had an excuse. Always made in ignorance, always trusting luck. Don't do that. If it's not legal and it's not safe, then don't do it.
Airplanes are mechanical, airplanes break. Accept that, and accept that repairs are necessary by qualified individuals performing to acceptable, legal standards. Cobbling things together isn't justifiable, nor safe. I've seen holes in exhausts wrapped up in beer cans and saety wire. I've seen duct tape used in ways you might not have believed possible. Not good. Not good at all. If you really want to be prepared for that flat tire, then carry a wheel assembly with you, ready to go. That's a lot of extra weight, and bulk, which is an inconvenience, so of course you won't. Unfortunately you appear ready to place safety second to convenience, and that's not way to make judgements in aviation.