I know three people who set out to do this @Simonstrousers and did. They specifically wanted a high flying, wealthy man that would allow them a great life where they wouldn't have to work.
Person 1 - He loves her way more than she loves him. He is public school educated and very well spoken, a range of interests, very down to earth, kind. She's working class, worked in a paint shop, lovely parents and sibling, but she has an edge that's hard to explain. She got a job at an oil company and meeting men was definitely a reason behind it. Never went to Uni though very bright with A grades and could have had her pick, her belief is it was too much work. He has a Masters and PhD. He asked her out and she very cruely rejected him. It was only when he met someone else she threw herself at him and he married her. Not a marriage I'd want and in truth I feel a bit sorry for him. She also passive aggressively puts him down all the time. Terrible dynamic. Occasionally she will admit she was jealous of all wealthy people had and wanted that for herself.
Person 2 - She was engaged and realized she'd likely always be the breadwinner with her community 20k year NHS job. He earned a bit less. She kicked him to the curb telling him she wanted someone with more potential, retrained, moved to London, applied for jobs in Canary Wharf and bagged her boss. A public educated, met the Queen at social events, very arrogant man who in truth wasn't very good looking or at ease socially and she is very bubbly, the life of the party, well liked instantly and confident. She had traits he I'm sure wishes he had. He's very anti social but very high income with parents that will die and leave him millions of inheritance. As soon as they were engaged she quit work and has never worked again. Lives in a 2 million pound home in the home counties, gardener, ironing lady, twice weekly cleaning lady, weekly dinner parties costing 500-800 and 3 dc in fee paying schools totaling 45k/year and rising as they get older. Honestly i would not swap lives, she has no equality in the relationship, she's there to please him and it is very much let me get you a drink the second he arrives home. He's away loads, not an involved parent though is better than she thought he'd be and part of me feels she sold so much of herself to marry him. Their home is immaculate and it is expected it is always to be that way, after all she doesn't "work" - his standards not mine. Even after the birth of all of her dc she was in a rush to get back to her perfect weight as he had started calling her "the whale". He wants a trophy wife and it's her job to be that. Not for all the tea in China would I do that.
Person 3 - also NHS worker, angry she didn't get a Dr. Joined dating agencies adn looked for older men (a decade +) who had never been married, had good jobs adn wanted to settle down. She met someone 12 years older, she's attractive and confident. At 40 he was shocked a career 28 year old wanted him. They married within a year and he dropped dead a year later.
I think people who set out to do this may be pleased with material things the rich men bring them. But of the three people I know above, none are truly happy. That's not me judging them, but things they've admitted. They use words to describe their marriage that are so telling.
Now, I think you can meet someone and this not be the case, whether they are wealthy or happen to become wealthy. It's the mindset of finding someone wealthy that seems to create a paradigm in a relationship I don't think most people would want.