Punctures less that 1/4" in the tread area can usually be safely repaired. Proper repair consists of both plugging and patching the puncture, or using a mushroom patch (combination patch+plug). The patch reseals the inner liner to prevent air from leaking, while the plug seals the outer layers to prevent moisture from getting into the belts/cords. The puncture must be plugged, the plug trimmed flush, then innerliner must be cleaned, buffed, cemented, patched and coated. Neither one by itself is considered ideal. This is official tire industry (Rubber Manufacturer's Association) "best practice." Most tire shops will follow this procedure, not only because it promises the best results, but because by following "best practice" it limits their liability should the repair fail resulting in an accident. But this is not a roadside repair, so from a survival perspective it is impractical. (Also note that many manufacturers consider the tire's speed rating void if it has been repaired, even following best practices.)

Plugs are coated with vulcanizing glue to provide an air-tight, water-tight seal. If applied correctly they can and do adequately fix most small punctures. I have driven on tires I've plugged myself, occasionally more than once, for months and years, until the tread was used up, without issues. Granted, I'm not driving a sports car at high speeds and G-forces, so your mileage may vary, but I do put on over 30k miles a year, mostly highway.

Going further, as I mentioned in past posts, I do a lot of off-roading. It is not uncommon to experience major cuts or punctures on the trail. I can tell you from practical experience that it is indeed possible to plug both larger tread punctures and even sidewall cuts. It will take lots of plugs. I think our club's current record is 30 plugs in one sidewall cut. The most I've personally seen is 12. No, it is not safe to drive at highways speeds. But it can be done in an emergency to get out of a hazardous situation and make it to someplace where the tire can be replaced while you wait in safety. I have seen fellow club members continue to use tires repaired with multiple plugs for months on the trail and for around-town driving. Not recommended, but it is an indication that even a horrible plug job can be used to get you to safety.

Finally, doing a roadside plug repair does not mean you can't then have the tire properly repaired. A single plug is one part of the ideal repair procedure. Once you can get a to a tire shop they can finish the job by trimming the plug and applying a patch. This means there is no downside to using a plug. Worst case is you have to use more than one plug to seal the hole, but that tire would require replacement anyway, so there's really no downside and the upside is you are mobile again, albeit at a slower rate with possibly limited range.

So in an ideal situation, where you have a spare and can safely change your tire then drive to a shop for repair, having the repair done properly with a plug and patch is the way to go. But if the situation is hazardous, a quick plug and air-up can get you going in minutes, then deal with the final repair later.

As for fix-a-flat, slime and other tire sealants, I have never seen them work, either. But I have seen them make a big mess that is time consuming to clean when the attempting to repair or change the tire.