when i use a media center, i prefere a silent one...
no active cooling, use passive cooling like Kodi
and no HDD, use a USB-Stick or SSD
i use LibreELEC, with a Heatsink case, but the flirc/kodi case seems to be a bit more effective in heat dissipation and looks nicer.
i can use the remote control of my TV to control theLibreELEC... passing CEC signals over HDMI cable.
but i use a RPi3B, at the moment. i have no need of 1Gb/s network and 4k for media center.
i never tried my new RPi4B as media center. it has also a Heatsink case and i never reached the temperature where is throttled down the speed.
playing DVD/BluRay i never tried on LibreELEC.
PVR i did via a USB TV receiver (SD & HD) (add-on TVHeadEnd PVR-Server).
watching live TV via TV card (SD & HD) no problem (add-on TvHeadEnd PVR-Client).
watching online TV, depends on the available add-ons and what you want to watch.
videos/pictures is no problem.
playing old games (add-ons, not always as performant as with Lakka/RetroPie, but mostely playable).
all add-ons are the official ones from LibreELEC & Kodi.
setting up the TvHeadEnd Server was a bit tricky, but once its done its ok.
all devices (USB-dongle for wireless Joysticks, USB-dongle for wireles keyboard/mouse, USB- TV card, USB-memory stick) are connected directly to the RPi (no external powered hub), but it depends what you connect.
my USB-BluRay drive will not work without external powered hub.