but why in the hell they never decided to spend it a 2nd joy-port
Because the vast majority of games are digital comics, RPGs, and simulations that require only 1 player.
That was certainly not the case in 1987. Action games were the priority at first, and that includes Bomberman.
I would say that they wanted the extra money, and also they wanted a 5 player focus. Making the system super small (which was a really "cool" thing to do with electronics in in 1980s Japan...still is) was probably a factor as well, but to a lesser extent.
I wouldn't be surprised if NEC had a part in that choice. They clearly loved making hardware. Just look at all of the (expensive) PCE products they released.
As for why Hudson went to NEC...its pretty simple. NEC is a mega huge electronics company with loads of factories, and experience, etc. It was probably a situation where either they could go with NEC, or they could attempt to raise the hundreds of millions of yen it would take to build a PC Engine factory (probably not an option). As I said, they tried Nintendo first, but they weren't turned on by the PCE.
Nowadays it would be simpler to just send the plans to a Chinese company and have them make it, but this was in the 80s before the Europeans, and the Japanese turned the Chinese and Mexicans into our $1 a day slaves. Things were still made in Japan by workers who earned a living wage.