First, I'd like to reiterate that it's better to drop the concept of shipyards than to retain shipyards, but make them cheap and plentiful. Rather than building and upgrading a shipyard on every industrial world, just assume that every industrial world has one, and move on.
On the question of complexity, I'm all for Occam's razor, but if shipyards are done right, they will greatly enhance gameplay.
The main gameplay benefit of a shipyard is to create a strategic focus. A focus for strategic investment, ship construction and fleet deployment. A big strategic target for enemy fleets and saboteurs and a catalyst for dramatic, game-changing events. The question of how much shipyard capacity to build and where it should go should be an important decision with long-term consequences.
A small quote from War of Honor, for some imagery...
Colonies in Moo2 have a tragic sameness to them. The solution is NOT to affix to each a long list of insignificant details, an 'each special in it's own trivial way' approach. Specialized planets are an important step away from that. Shipyards should also help, each shipyard world vital due to the colosal investment you have made there, the focus of the industrial production of a dozen worlds.His eyes were on the visual display, not the tactical display or the maneuvering plot. He was staring at the huge naval yard, its individual structures long invisible as they fell away astern, and his eyes were cold and empty as space itself.
And then his mouth tightened and pain flickered in those empty eyes as the first small, intolerably bright sun flashed behind his ships. Then another. Another, and another, and yet another as a tidal wave of flame marched through the huge, sprawling naval base Manticore had spent almost two decades building up from literally nothing.
Those silent pinpricks looked tiny and harmless from this range, but Higgins' mind's eyes saw them perfectly, knew their reality. It watched the forest fire of old-fashioned nukes—his own missiles' warheads, not even the enemy's—consuming fabrication centers, orbital smelters, reclamation yards, stores stations, orbital magazines, the huge hydrogen farm, sensor platforms and relays, and System Control's ultra-modern command station. And the ships. The handful of ships in the repair yards. The ones who'd had the misfortune to choose this particular moment to be immobilized in yard hands because they required some minor repair, or to be undergoing refit. And worse—far worse—the magnificent new ships. Twenty-seven more Medusa-class SD(P)s, nineteen CLACs, and no less than forty-six of the new Invictus-class superdreadnoughts. Ninety-two capital ships—almost six hundred and seventy million tons of new construction. Not just a fleet, but an entire navy's worth of the most modern designs in space, helpless as they lay beside fitting-out stations or half-finished, cocooned in their building slips and dispersed yards.
So, down to brass tacks. I don't see why upgrading shipyards should be such a chore, especially when the upgrades (like the shipyards themselves) are few and significant. If each step doubles the size, it's not going to keep you busy unless you are building up a new one in late game, in which case you can just select the end size you want.
Shipyards also don't have to be complex. We are talking about a capacity that doubles with each Level, and maybe one other rating. As long as they are few, shipyards will be simpler than building ships on a large fraction of industrial planets.
As to the idea of having a shipyard-designated planet devote a constant fraction of it's industry to building and maintaining a shipyard, I think it can work (especially if the fraction is large). There would need to be some mechanism to grow the shipyard over time so that you can't switch the shipyard on-and-off like a light-switch, but there are many good ways we could do that. Probably the simplest is to dedicate the 'shipyard fraction' that's not consumed by maintenance of the shipyard to expanding capacity. I'll have to think about it some more.
One last note on macro-management tools. I think its a good idea to make the game as manageable as possible without macro-management tools. The player should never be forced to use these tools, especially if tool AI is making potentially vital decisions such as what ship to build where.