I don't have experience with person to person.trading but so far O thought this was one of the safest way because you meet the person you are dealing with so there is less possibility to get scamed. Never thought that you could be robbed.
You can be robbed any time, thats why holding too much cash in your walet is dangerous. The OP example someone hold 28000 in a wallet without security guards is pure insanity, no matter whether wanted to buy Bitcoin or something else.
I do use localbitcoins to buy Bitcoins in person, but never in larger amounts. Carry in your wallet only as much cash as you are ok to lose if you get robbed, but I talking from my experience when someone stole my wallet and I noticed it later (and it has nothing to do with Bitcoin).