A dreamy guy but he's kinda stingy..?

I've been dating this guy for a month now & I couldn't ask for a better bf: he's well-educated, got a nice managerial job, has his own house, he drives a cadillac escalade to work, he has this vintage sports car -a 1965 replica shelby cobra sitting by his garage, he wears a Tag watch, in short, he's very upscale. I don't really like him that much bec there's this Airforce guy I was really eyeing on but my bf was more pursuing & he's really good in the sack, as in, really good in the sack & he treats me like a princess- goes to his knees to help me put on my boots, goes to my work just to give me a goodnight kiss before he goes home from work, he kisses me on the forehead & puts blanket on me when I'm sleeping, he'd make sure I have my towel ready when i get off his shower, gives me wonderful hugs & kisses & all other sweet, thoughtful stuff. But the only one thing I was wondering about was he never asks me out like u know, dine out, go to clubs. One time he asked me to come over his office so we could have margarita at this upscale bar but we never made it coz i was late but he opened a nice bottle of Taittinger champagne at home & we sipped that while we lay on his couch watching TV. But even if i'll be the one to ask him that we see a movie bec i have tickets already, he wouldn't want to go & would make an excuse that he's tired so most of the time we just hang out at his house, watch DVD & make love. In the morning he'd never attempt to make breakfast for the both of us, just coffee coz he's always hurrying to work. Most weekend mornings when his 5-year-old daughter's at his place, he'd invite me over to join them for coffee so I'll be the one to bring in breakfast. When he spent his first night at my apartment, I don't want him to leave until we had breakfast first, hoping he'd get it that sharing a meal even if it's just a McD meal is part of the dating thing & that he needs to give a little efffort when we're at his place to cook dinner for us. He made me dinner once during the first time I visited but that was it. No repeat whatsoever. I'm not really into guys treating me or always taking the tab for me bec I do well on my own & I'm also generous & have the sensitivity to take turns. It's just that I'm wondering why he's so stingy. He shared with me that he's suffering from a legal battle with his ex- the mom of his daughter & that he's also giving child support and then he said he's got all the bills he need to pay. Date with us would just be hiking & just staying home. Is this a healthy relationship?