It goes without saying that air cover and air support are critical to war success, but from it's inception, the suggestion that airpower alone could bring success to the battlefield had proven very costly (especially to taxpayers...)
Douhet, an Italian air force general, designed the concept of strategic bombing, explicitly formulated as razing cities to the ground with their inhabitants. It's the understatement of the century that this concept proved hard to achieve by the Mussolinian war machine, even against Ethiopia and lavish use of yperite. Mockeries toward Italian aircraft aside, the thing is that is that the concept was not spectaculary more working even with the immensely more powerful US industry and B-19/B-29 fleets.
The Allies bombing campaign against Germany certainly worked, but not in way envisaged by strategists : it was a grueling war of attrition that came with ghastly costs in aircrews and machines. Forcing the Nazis to pin down in Germany hundreds of badly needed fighters, ten of thousands of AA guns did at least as much damage to their warmachine than the actual bombing-with the side effect that bombing was never as safe as promised-being an aircrew in the RAF Bomber Command was actually riskier than being a WW1 infantrymen.
(But Sarah, Japan ? Japan was virtually defenceless against B-29s raids, yes, but this was the result of an very efficient blockade that crippled fighter production to a way that could never have been achieved with Germany-it's way easier to sink freighters from an ennemy that does not care about ASW than destroy completely factories. The B-29s would have been more useful at dropping mines than napalm, which was something that LeMay was against-the former, not the later)
Morale collapse and rising against the regime, despite being premises of the whole thing, never came.
TLDR : throwing at the enemy more machines and more airmen than he can throw AA guns, nightfighers and radar against and slowly erode it's capacities, a perfectly legit strategy, is nevertheless completely different that what was excepted (''our vast fleet of bombers will lay waste to the ennemy and make him surrender while avoiding those costly land battles'')
That's for strategic use of aircraft. But even tactically, the results of air bombing tend to have been dramatically overstated against anyone but completely inept or demoralized ennemies.
Two examples (beyond the classics, like Vietnam, were deluge of bombs were required to dislodge the enemy-''but it was a jungle'' is not an excuse, since it required massive amounts of bombers to make an impression on North Korean/Chinese forces operation in the quite jungless North Korea)
In 1940, the decisive Axis breakthrough against the French occured near Sedan. Two utterly demoralized, badly trained, with virtually no air support and in fact almost none AA guns, French reservist divisions, in addition of facing an entire panzer corps, were bombed with impunity by over 1500 Luftwaffe bombers (level and dive) for several hours. While one division panicked, the entire ordeal (including several missions by virtually the entire Stuka force) did not actually knocked a single hastily made French bunker and killed maybe 50-100 French soldiers (this is not a typo : fifty to one hundred)
The widely mocked (and rightfully mocked) Iraqi army actually survived to a surprising degree the onslaught in the KTO by simple basic measure like wooden beams and sand bags-the deluge of bombs and missiles, even smart and guided ones knocked down maybe 20% of Iraqi heavy weapons and AFVs. And this is an average : poorly motivated Shia infantry divisions took the brunt of it, while ''elite'' (very poor by Western standard, but still) Republican Guard divisions came out almost unscathed
(Note that airpower was, like in WW2, absolutely devastating against supply lines Be it with an Hawker Typhoon or an F-16, it's way easier to blow up a convoy of lorries than even an obsolete tank, dug in or under cover)
- - - Updated - - -
TDLR : a Douhetian conception is in fancier terms ''bomb them back to stone age'', which, in addition to edgelords, was more or less the tactic pushed for in Germany, Japan, Korea, Indochina. It does not work very well compared to the cost involved. Even tactical use of aircraft is not as easy as assumed by proponents of air power, especially against minimally competent foes (exemple : the Serb army against NATO bombardements )