I think +10 to Intelligence checks seem too high. It's equivalent to someone having a 30 intelligence in regards to that topic. I think +5 would be better as it means someone that has a 20 Intelligence would just as likely no the knowledge regardless if they have had training in that particular area.
I thought so too, but don't be deceived by the number.
Knowledge skills really work differently from other skills. All that matters, is the
difference between someone trained in e.g. Knowledge Arcana and the others who are untrained.
The Intelligence bonus actually gets in the way a bit, because it makes it just as easy for an Int 18 genius to know something about Arcana without having read a single book, compared to someone with +4 skill bonus.
It's not the same as jumping or climbing... If I've never climbed a tree, I can still try. Physical skills are natural.
But Knowledge/Lore skills represent already knowing something. Here there is room for a lot of debate, how did you get that lore? Did you read books, did someone tell you, did you listen to bards in tavers, is this lore just part of folklore? You can have a fantasy setting where libraries abound in every city like today's real world, or another fantasy setting where books are as rare as in historical middle ages.
Maybe we shouldn't assume or think too much, but I want to point out once again that the danger is in allowing everybody to roll for Lore checks. This issue has been acknowledged since 3.0: "An untrained Knowledge check is simply an Intelligence check. Without actual training, a character only knows common knowledge." This allowed the DM to occasionally allow some PC to try a Kn:Arcana check especially if
no one else in the party had that skill trained, but it generally was meant so that the DM would only let the trained PC do the check... otherwise every single time every PC would try their chances. And if you have 1 trained PC and 4 untrained PCs all of them rolling, but the difference in bonus is small, it easily ends up with the "rest of the group" (together) succeeding more often than the specialist.
To me this +10 idea seems to be meant for the same purpose, i.e. to tell untrained PCs to not bother rolling, and just let the specialist take the spotlight.
If it was for me, I'd just go straight to the point and simply make all Knowledge checks "trained only", but apparently they want to keep an open door.