On difficulties above Emperor, you'll always be behind in tech at the start, when you want to be attacking with Assyria, and as anyone you always want libraries.
It's also a misconception that you want to be behind with Assyria - in fact you want to be close to tech leader,
The siege tower is powerful out of context, but it is not sufficient compensation for having no ranged siege units. You need several, or a couple of supporting melee units, to get the most from it, and you still can't skimp on ranged units. Unlike the Hun battering ram, the siege tower costs you the catapult, a long-lived unit at a critical game stage, and having no ranged siege before Physics is tough. Especially as the siege tower's effectiveness as a direct siege unit (rather than to support other units) tails off before the catapult's.
The Royal Library has very little synergy with the civ's approach. It requires a Great Work of Writing, and you don't want to be devoting effort to teching to Drama and Poetry and then building a Writers' Guild early, plus the experience boost is less than you get from a barracks. So either you use it late, or you try to rely on looting a Great Work from a captured city. In either case, it's a somewhat pointless bonus since by that time you've built the units you need (particularly if you're successfully capturing cities).