We can discuss this indefinitely, but the fact remains that a folding knife's vertical blade play can be boiled down to two criteria: Safety and Performance. A knife with a good deal of vertical blade play or weak lock up can slip its lock and fold on your fingers. This is why Lynn Thomson's guys make a big deal about doing pull ups on the knife to test the lock strength. A knife with a good deal of up and down play may disengage the lock. A blade wiggling from side to side would bug me a great deal. A knife snapping shut on me when it's not suppose to could ruin my day.
As for performance, this gets into the weeds of perception. Vertical blade play can make a knife "feel" like it's not doing the cutting job or requires extra effort. OTF autos have more blade play than would be acceptable for most knives simply due to the design. A $300 Microtech does not lock up as tight as my 12 year old $70 Endura. However, it is baked into the design. My Microtech cuts just fine, but when I bear down on it, I can feel it move a smidge.
There is actually a thread about blade play on the CRK forum. Probably the most exacting production knives out there in most regards. I believe someone mentioned a tolerance of .0005 or some such to account for the grease between the tang and washers. My Inkosi is dialed in to be smooth to open and close with no detectable up and down play and only the faintest side to side if I flex it hard enough to cut myself (which I did). I can crank it a touch tighter and it doesn't budge in the least. Maybe in a vice, but not using my arm strength. However, when I do that it opens like a wooden door with water damage.
I'm not sure you can reinforce a folding knife enough to make lateral play go away to the point where it is both undetectable and doesn't hinder the function of a knife. A solid frame of expertly milled and finished titanium using a ceramic bearing and washers tightened down by a big ol stainless screw and bushing comes about as close as I have held to "zero" lateral play.