Are the stats of the lowborns good? Besides, the main reason to get married is to have kids and to increase the size of the demense limit. Of course, you can marry for claims, but I personally will still choose a lowborn with a good Stewardship score and traits over the daughter of the HRE Emperor with ok stats and traits.
As for opinion boost, you will only get it if your vassal's ambition at the point of marriage is to get married.
No, the stats of those Lowborns vary but are often horrible. At the same time, purpleborn princesses of BYZ and genius courtiers from countless principalities in Italy and the HRE are readily available to anybody. It's basically the matter of the AI character not looking outside its own court.
I'm pretty sure they stay lowborn, seems like I saw this one time and that's what happened lol, that is if you don't legitimize the thing.
This is off-topic but I would like to warn you guys that when a lowborn, bastard or not, succeeds to a duchy (not sure about lower titles), he will receive a random name and shield. Learnt it the hard way when I betrothed one matrilineally to a young daughter and he succeeded in the meantime.
Kate Middleton is a lowborn, no one is bothered by that.
Well, most of us are lowborns ourselves, we just care for our blue-blooded petlings in CK2.
French and English nobles cared little about the mother's nobility (noble quarters etc.), focusing on the father but in other European countries it tended to be more important. Thus, it's far less surprising to see somebody male from France or England marry down a few notches. Or even somebody female, as proper nobility is tightly restricted anyway (just to the actual peers).
Plus, Kate's dad was technically made a courtier with a generic dynasty before the wedding. (Although I'd say they had a strong working class background.) Not only she herself but her dad, actually, mind you, allowing the status to descend on the daughters in second generation as opposed to being a new grant specifically made to Kate.
The English system is a mess these days anyway, not like it was ever clear before (may've been even messier in the past centuries). In late middle ages and afterwards, "gentility" was to them what the continent or even Scotland regarded nobility as. Therefore, the only nobles in the realm are peers and not even their wives or children (including eldest sons). It's debatable whether royals and by this I mean sons of a king, before they receive a peerage (which is when they marry, at least typically), are actually proper nobles under their bizarre rules. At the same time, the requirements for "gentility" have relaxed over centuries, changing from old families (landowners going back to William the Conqueror etc.) through anybody with land or education or some noble occupation, to anybody who could avoid manual labour (with some vagueness as to merchants), eventually "gentleman" (tied to "mister" before surname) being any lowest clerk or similar figure, and finally any man.
Also, if you graduate from a posh university with one of the qualified degrees (including MA), get admitted to the bar or rise to captain (army, not navy), you're not even a simple gentleman but an esquire just like a knight's eldest son. Esquire corresponds to basic nobility ranks in continental Europe, especially the French ecuyer (base rank for any noble) or German edle. Doctors and colonels get even higher than that (technically being serjeants).
So, they manage to blend a hardcore restrictive aristocratic system with a democratic approach in their own twisted way.
For the record, Kate doesn't have strikingly bad stats or traits, ugly portrait or 10 years of age on William. This makes him already much better off than many royal heirs in current CK2.