There is another problem with modern televisions with regards to consoles and gaming devices that you haven’t mentioned.
Most old games consoles, including the original Playstation don’t provide a true interlaced video signal – they only provide field 1 – twice and signal as such. Older analogue televisions (and video recorders) dutifully repeated this but some modern digital display devices don’t like this at all as it technically doesn’t conform strictly to the specified video standard (be it the NTSC standard used on American/Japanese consoles or PAL, used in Europe – it applies to both).
I first came across this as a problem when working in the BBC around 2000 – we wanted to record a small clip from Crash Team Racing and a couple of other PS1 games as an example of what was then modern gaming, but the Digibeta video recorder we were using point blank refused to even acknowledge there was a signal coming in on the analog input.
I got round the problem by using a professional video standards converter we happened to have in the office. I found that if we set the input and output of the device to the console’s video output standard (in our case PAL) it would correct the field problem and thus the digital video recorder would record the previously non-standard output of the console.
I believe this problem is also why many modern flat screen displays are unable to display the output from many older, perfectly functioning games consoles.
Sadly not a cheap solution to go down as the standards converter was worth several thousand dollars…