Patrick Stewart doesn't need money to get a hot young girlfriend, he has presence and working in theatre he would be surrounded by them.
They probably resisted giving Picard too many love interests simply because they need to give Riker something to do.
What someone told me on startrek.com was that when he was in a play, Sir Patrick Stewart had an arrangement with the Stage Hands, where he would give them a signal by quickly licking his index finger and then pointing with it at some hotty he fancied out in the audience. Then one of them would approach her with a pass and invite her backstage to meet Patrick in his dressing room. He'd chat her up a bit and if she passed the preliminaries, he'd just take things from there. Or, if he had to do an encore, or something, he'd give her the address to whatever hotel he was staying at, if the show wasn't local and unleash his irresistable charm on her ... the man's insatiable!