One would think a factory made uke would be more consistent, especially where laminated woods are used.
Not at all, unfortunately. The biggest problem on almost all factory ukes is that they are typically delivered with actions that are intentionally high - apparently going by the theory that it is better to have a uke with poor intonation than one that buzzes. Nuts are molded plastic and no one ever checks to see how the strings seat, what the action is like at the first fret, etc. Since they aren't going to spend the money to have an experienced technician adjust the slots by hand, they default to anywhere from high to very high.
You almost always have to touch up the slots in a nut on a factory uke whether it is laminated or solid wood. Exceptions are the Mainland ukes (because Mike and Tootka do that up in Indiana before they ship them) and factory ukes purchased from outfits like HMS, Mim, Uke Republic, etc.
It's not that you'll
never get a good factory uke from a big box store or ebay drop shipper - I once got an inexpensive Lanikai 8-string acoustic electric with perfect intonation at the first fret from an eBay drop shipper - but it's really a crap shoot.
The next big problem on factory ukes is they are often overbuilt. You would think that would be a good thing but it is not in an acoustic instrument. Overbuilt means tops are too thick, bracing too heavy, and glue is often slopped on with a trowel. The result is an instrument with little volume, sustain, or tonal complexity. Unfortunately, there really isn't any fix for this. That same Lanikai 8-string played well plugged in but had all the acoustic character of stroking a wet dog. It was so bad I couldn't bring myself to stick someone with it by selling it so I gave it away. Generally, overbuilding will be less of an issue at the higher end (solid wood) ukes in a factory line. They still aren't anything like a Hawaiian uke with the occasional rare exception but they are generally pleasing to play once set up.
My recommendation for someone in the ~$200-300 (depending on size) range is a Mainland (in spite of the rope binding) or an Ohanna or Kala set up by a pro like MGM at HMS, Mim, Mike at Uke Republic, etc.
When you get into the KoAloha-Kanilea-Kamaka range you usually can buy with confidence without worrying about whether the uke has been set up because they do that in the shop before they send them to dealers. The action may not be perfect for you (I find KoAloha actions to be a little high at the bridge end) but they will be very playable, well intonated, and have volume, sustain, and tonal character not generally matched by even the solid "factory" ukes.
Then, you can get into the luthier built stuff where you should expect near perfection in every category.
John