I've made my views on these matters pretty well known elsewhere already. I think it is no accident the White leadership (by which I mean the various generals and admirals and military types generally) was so narrow-minded, fractious, vain, and impolitic. It reflects their class position, as champions of an order basically founded on brutality.
I'd rather wonder why the SRs couldn't come up with champions from their own ranks; with enough military strength deriving from peasants and their sympathizers, I suppose they could get some use out of these uniformed thugs without being overwhelmed by them. I obviously think it is no chance accident it was the Bolsheviks who prevailed.
For Kolchak to have done differently I suppose he would have had to have been a different sort of person. Show me a former Tsarist officer who actually looked forward to the sort of Russia the SRs wanted and then I'll be happy to follow along a timeline that has that amalgam of agrarian socialists and progressive-minded Old Regimists (if you can show that's not an oxymoron to this skeptic!) If the principle is that the majority ought to prevail, and the peasants of Russia were the majority, then you've imagined a different sort of Russia than the old regime was.
I have the impression that if you want a statesmanlike, flexible, forward-looking White, Wrangel was closer to it than any of the others. Probably still not close enough.
Anyway, suppose they do win. The Bolsheviks die or flee into exile. The Old Regimists make their peace with a Russia run mainly in the interests of the peasantry, and the peasantry mainly wants to raise crops and buy imported goods by selling them on the global market. Such a Russia might well be better fed, and might even support a shrunken sort of industrial sector. If anyone tried to make really big profits on Russian industry along capitalist lines, they'd have to deal with a workforce that had just recently come from the land, still has ties in their various home villages and towns, and can go back there if they don't like the pay or working conditions. But even granting that OTL Stalinist policies failed to make the best use of the country's agricultural capability (because priority one was to get control over the countryside, priority two very close behind was to extort enough food and other agricultural products to support massive new industrial developments) does Russia have enough good land to support a bucolic Utopia? If they do in say 1921, do they still in 1941 after the population grows? If not, you'll have your hungry and desperate workforce available to work in new factories and mines on a profit basis--but by that same token, you'd also have fertile ground for a new edition of the Bolsheviks, rising from the same origins they did before the Great War.
But if the land is good enough that honest work and getting to keep the fruit of one's labors on the land leaves the countryside well off enough, then I don't see much of an industrial workforce choosing urban labor at low enough wages to make Russian industry an attractive investment. If Russia is dependent on foreign industrial powers for all their higher-tech goods, from harvesting combines to pianos, how long will it be before predatory Western nations seek to gain control of the country and leave the peasantry not much better off than they would be under Stalin?
I actually suspect that part of the character of the reactionary, intransigently conservative Whites was a recognition of this basic reality. Someone was going to extort the fruits of their labor out of the Russian peasantry, if not a native Russian aristocracy than a foreign one, or a corrupted SR leadership bought out by foreign intrigue. Thus on one hand the Whites were themselves overwhelmingly dependent on foreign support to be as viable as they were (why not be the one who sells out, if someone inevitably must?) and on the other had no patience for any third ways. The Bolsheviks were their opponents because only they had a vision for how Russia could survive and compete with the more-developed Western nations without essentially knuckling under to them; the moderate alternative to the extreme left was not some benign Shire of the peasantry but a return to the old regime, which was at least Russian.
How Russian it would have remained, if the Whites largely owed their victory to interventionist foreign powers supplying them, I leave as an exercise to those with patience or enthusiasm for such regimes. I would be more interested in someone showing how an agrarian-based party could parley their inherently dispersed and less-educated base into something sophisticated and mobilized enough to stand up to the various rival interests, and find the balance between foreign trade without which they'd have to pursue more or less Stalinist policies to have anything modern, versus the foreign influence that comes with it, and work out the best deal for the typical Russian peasant. If they can do that, I suppose Russia will develop at a slow pace; can such a Russia deter foreign invasion by a combination of sheer mass and inoffensiveness?