50% casus belli cost on a level 1 martial lifestyle perk. Wars cost piety, but the combat therein can also grant piety. A pilgrimage every 15 years can give +600 piety in one go. And it's possible to pick up common clusters of piety here or there that add up all together. Gonna be some pretty smooth kingdom-level conquests.
Fervor loss doesn't mean much either. It dips from holy wars, then bounces back up either whenever the heresy fires or when good priests get their headpats. Actually converting the heathen lands I mass-conquer, even without infinite kingdom holy wars, is a non-issue since at most you risk an easy peasant revolt, if they even hit enough military power to fire.
Look upon the piety I gain from a battle in an offensive holy war of my own; behold and see that it is none.
Bellum Justum will certainly help in affording multiple wars (in terms of piety and prestige, anyhow) - that's what it's supposed to do. The highest piety gain from pilgrimages are from the very long ones, which are fairly expensive, particularly in early game when you haven't had the chance to fully build up your economy, and doubly so when you're waging large scale wars every opportunity you get - war costs money, too, and a fair bit of it. If you do manage to do both, wage kingdom level holy wars every chance you get and go on very long pilgrimages, I find it unlikely that you'll afford to improve your demesne as well. With your piety going to wars, you can't ask your head of faith for money, either.
And you do realize, the more land you rapidly conquer, the more powerful revolts become - it is not made easier by the ability to wage multiple kingdom-level holy wars, quite contrary. And even if these wars are simple to deal with, they cost you - both for the upkeep of your armies, and for the loss of levies and tax due to reduced control. With hostile land, your vassals will acquiescent to peasant revolts, and enter a death spiral where their productivity towards you nears zero. And populist revolts encompassing all of your recently conquered territory
will fire while you're busy fighting yet another kingdom-level holy war, stretching your armies thin.
I am not saying it's impossible to wage multiple kingdom level wars with one character with this tradition - that would make the tradition almost entirely pointless - but it's not trivial either, it comes with opportunity costs, and the risks of overextension.