Personally, I found I was more tolerant of side play when knives cost less money. If I am paying extra money for a knife to be made by people who claim their products are of greater value, they should demonstrate this additional value in superior materials, fit and finish.
I'm pretty much the same. The most recent Case I purchased was a Bose teardrop jack in ebony. It has a bit of wiggle. It's a bit irksome, but I can live with it considering the price. The last several GECs I've purchased (a few F&Fs, a 13 congress, and a 48 Weasel) are rock solid. Actually, the most recent Case I bought was a chestnut CV peanut, and it was rock solid, but the main blade was proud when closed so I had to return it.
I probably won't be buying any more Cases unless there's something special. GEC has been knocking it out of the park lately.
In response to the OP's question, the reason, to me, in my mind, is that a traditional knife is representative of an age of pride in craftsmanship. Blade wobble means a lack of that. A wobbly blade, as long as it's not too wobbly, doesn't really affect function. A bad liner lock or framelock is different because these are different knives with different mechanics used in a different way. When I open and close (and open and close and open and close) my 48 Weasel, I can feel that the people that made this knife made it with the pride that they made a quality knife. But when i get a Case where the blade wobbles or there's gaps in the liners or the blade grind is crap, I can feel that it was made on an assembly line by people that don't give a damn.
From my own personal perspective, I take pride in what I do, although it's rather insignificant. I make pizzas for an international chain. The food is...mediocre. I have no control over that. But I make a damn good looking pizza with it. I make them better than the ones you see on the menus and TV ads. My co-workers - some of them make great pizzas too, some of them make garbage. But when I make you a pizza, I make it good. Even if you were a jerk or idiot on the phone, I do my job and I do it to the best of my ability. Because as insignificant as it is it's still my "craft" and I take pride in it. You're eating something that I crafted by hand, and I don't want me or my name to be associated with an inferior product.
That's how I feel about the knives I buy and carry.