> Female lawyers and female doctors are fairly common in media.

Now, yes, but what about in the 60's and 70's?

How many engineers are represented in the media in general? Has there been a hit TV show with male engineers as the main character?

How big a hit? Halt and Catch Fire fictionalized a lot but two of the four leads were software and hardware engineers, The Expanse has the primary hardware/software hacker on the ship as one of the four main characters but it's a woman, Person of Interest had two of the four main characters be software programmers, one a man and one a woman, Mr Robot has software developers for most roles besides gangster and law enforcement, one of the four or five primary characters on 12 Monkeys was a scientist/engineer but a woman, Westworld has the scientist as the main human character for the first season and a different one for the second, most of what they do looks like software programming, Chernobyl showed a lot of engineers in the nuclear control room, trying to fix things afterwards.

There's also McGyver, Neo & Trinity, Rey also doesn't seem to have her thumb in the middle of her hand, David Lightman, Tony Stark--in fact, Marvel is chock full of male engineering types; Beast, Hulk, Reed Richards, Peter Parker.

The examples are legion.

You can add in Fast and Furious 6+ (lol)

There are plenty of female lawyers and doctors who aren't main characters in television shows, and where being a lawyer or doctor is not a defining characteristic of how feminine they are.

The same cannot be said for the legion "quirky female hacker" characters that exist in many TV shows.

Big bang theory, for example, has mostly male nerds. The core Silicon Valley engineering team is male. There are of course exceptions but male and female engineers are not represented equally in media.

Big Bang Theory first season maybe. Ultimately they were almost parity.

But what should they represent? The real world, some fictional idealistic world? If so, whose idealistic world should tv shows represent?

Depending on exactly what you mean, mythbusters or Mr. Robot count.