Why is it not possible to connect regular smartphone to my TV via micro USB?

[AC Question]

Lately I have been thinking about this and haven't found answer anywhere.
By the question I'm not referring to the phones with MHL or phones supporting USB 3.0, but regular micro USB 2.0 available on almost all android smartphones. It seems to be fast enough to send picture from the smartphone's screen to the HDMI port on my TV for example. (I'm not expert in this though.. That's why I'm writing here. )

I know that micro USB port has less pins than HDMI and generally is not built for sending picture, but shouldn't it be possible to program some tool for the phone that convert's picture from the phone's screen to sends it via normal micro USB 2.0 to some kind of driver board translating and forwarding it to HDMI port of my TV? ...so at the end it would work like a Chromecast but via cable and with much less lag... Would it be possible to make something like this?

 

[Rukbat]

but shouldn't it be possible to program some tool for the phone that convert's picture from the phone's screen to sends it via normal micro USB 2.0 to some kind of driver board translating and forwarding it to HDMI port of my TV?

There are - they're called MHL cables.

Would it be possible to make something like this?

Sure, but it's much easier to buy it already made.

(Remember - USB has only 2 data pins - a single channel. You have to encode audio and video on that channel and send it to the "board" [the MHL cable] in real time. You can't. Which is why phones have extra pins for MHL output.)