You are not being unreasonable. You know your child. You know your household dynamics.
Cautionary tale? Not everyone knows their child has an addictive personality. Although I have one, I didn't assume he would automatically have one and until gaming, I never knew he had one. Little late when we had the Wii.
We controlled everything. Only at the weekends, cut off wifi after hours, locked Ipad to certain websites, but can't lock youtube because they also use it for homework. We allowed Xbox, still only at Weekends. Allowed him to play with his sister, so his sister could play at her times, but any game would do by this time for his fix. We most recently moved to PS4 because all his friends have one (2 years later and only because we couldn't figure out what to get him for his 16th, it's the only thing he consistently asked for). We gave in. We confiscated all consoles until after his exams (made not much difference).
He's had the use of consoles since he was 6 in one way or another. We play the Sims also. But I refused to buy the most recent one and our computer can no longer manage the old one.
Yesterday he didn't play the PS4 at all. But I noticed him on his PSVita (for about 3 hours glued), bought with his birthday money. He didn't even know how long he was on it for when I asked. I monitored it to see when he would stop. If we don't take away the phone at night he's on it.
A few weeks ago DH caught him just going to bed at 2.30a.m. a school night (went back down after we all went to bed), after playing PS4 (he sure as hell wasn't socialising). We felt we were successful, because we were able to stop him playing for less time than all his friends. However, he has no self-control. So my monitoring for him is no good and neither is his self-regulation. He plays a sport and another activity, but thinks nothing of sitting in front of the screen all day. And if he's asked to get off one he moves to another.
Many on this thread haven't got to my stage yet. For me buying a £200+ product because all his friends have it, otherwise he will stigmatised, bullied, is why our children are so emotionally weak and maybe going old school with our parenting isn't all that bad - what happened to that old saying 'if [inset name here] jumped over a cliff would you too?'. They do not have the fortitude to make it in the real world which is fine for as long as they're under our roofs. Not so much when they have to do it all for themselves. Way to keep them dependent!
Yes there are children who will not have a problem (and astonishingly they will all be related to mums saying YABU).
You know YOUR child. None of our opinions should matter. I don't think you are being unreasonable. If I had my time, I would keep telling him what I've always told him. "Be independent. Have your own mind, do not follow the crowd." Then I wouldn't buy anything (even though I loved the Wii).
Oh and these people saying you want to live in the 19Century. RTFT. OP has enough tech in her house. She doesn't think she necessarily needs more.