This also would solve the issue of being a new player and not knowing what kind of major lines there are.
We use an "info sheet" for newbies on what all the cards are (not just major lines, but also service bounties and hotels). We also try to cover each tycoon card before starting, since it is nearly impossible to ask about your tycoon after the game start without tipping off who you have.
I haven't found the major lines to be a problem. In a game with limited luck, the major lines and service bounties add a reasonable level of luck. As long as everyone knows where they are, they can be factored into building decisions. We haven't found either type of card to unfairly or randomly create winners.
I wouldn't do it for the newbie factor, but you if you want less luck in your games, it would still be a game without the lines.