It's all subjective. 300k a year may not be wealthy to you, but considered wealthy by someone else.
I think the best way to put this is; being a doctor will put in you in position to be a top 3% earner in the United States. Whether or not you consider earning more than the other 97-99% wealthy or not..well that's just personal.
I think what a lot of undergrads fail to realize though, becoming a doctor is the surest way to earning a substantial amount of money; i.e. more than about 295 million other Americans. Climbing the corporate ladder is a complete roll of the dice. For every corporate bigwig there are 10,000 cubicle farmer's who would be estatic to make 100k a year.
I agree with all of this. "Being wealthy is being richer than your brother-in-law." If you end up making a big salary, chances are you'll be around those who also make a big salary. You'll move into a neighborhood of people making the same salary, and you'll work with those making the same salary. Once basic needs are met, happiness contingent upon wealth is entirely based upon comparisons to other people. If you live in a middle class neighborhood, you'll never feel bad that you don't have a yacht. Live in a gated community? You might be a little dissatisfied with your 300K/year. My grandpa always said it's better to be the wealthiest man in a poor neighborhood than the poorest man in a rich neighborhood. The moral is, do something that will make you happy for the 9-10 hours you're at work, and make sure everyone around you is poorer than you at home, or something like that...
As far as the rolls of the dice, getting a top income can be accomplished one of a few ways in a couple of industries. This list is a good start of
reasonably possible ways to earn big money (200K+), but is far from exhaustive.
1) Get into sales, work
very hard and long hours (many clients), work up the chain and make tons off of commission, selling only premium items.
2) Get into finance at big name companies. Be
forced to work very hard and long hours.
3) Get a professional degree (med/law/dental/etc) and join a practice/firm, or find a big name corporate entity willing to pay big bucks.
4) Get a job in petroleum engineering. These guys, particularly the drill managers, make upwards of 300K per year.
5) Join a company and work your way up the corporate ladder with "vacuum" leadership. Apply to any position above yours that opens, regardless of your interest in it.
6) Start your own business, preferably one that requires little investment and immediate returns (e.g. software, simple commodities, etc...)
Not included are the unreasonably possible, such as making it in acting, art, sports, etc... Of these, the most sure are medical/dental and law/finance. They require "initiation" into their world so-to-speak, and after attaining acceptance into that world (med school/dental school or top law firms/top financial companies) you obtain access to those salaries. The rest require full commitment as a career for many years. None ensure that you will be unbelievably wealthy, rather, each ensures that you will have the income necessary to be very wealthy if you invest your money well. If you make an extra 10K/year in investments beyond your expected gains and budget you can do something additional every year such as get an addition on your house, take an expensive trip, buy a much nicer car than you would have otherwise, etc...