Well, among fans that seems to be the case yes. Managers seem less interested. Venables, who had been out of a job for three years, got the job after Kevin Keegan, Ron Atkinson and Howard Wilkinson said "lol, no, I'm managing Newcastle/Villa/Leeds".
When Venables left hthe England job, the FA...
I imagine he would not be too keen on that job. Not a lot of managers take a thriving career and throw it away to take the part-time job it is to coach a national team. Goes for Howe as well - why would he leave Newcastle to manage England?
Also think there is 0 percent chance of FA headhunting...