I just had a cursory look at that FIFA list. Two of Brady's contempories are included, Ceulemans and Dalgleish. Brady polled better than both of them in the European Footballer of the Year (Ballon d'Or). Ceulemans in particular, only registered on the list two years in a row at 5th and 21st.
Tets provided this link once before (at least)
http://www.rsssf.com/miscellaneous/europa-poy.html
Brady
1979 7th
1980 8th
1981 9th
1983 23rd
Other honourable mentions
1972 Giles 18th
1975 Givens 27th
1977 Heighway 10th
1980 O'Leary 22nd
1981 Stapleton 21st
1989 Bonner 17th
1991 McGrath 13th
1990 McGrath 12th
1993 McGrath 26th
1999 Keane 6th
2000 Keane 27th
We haven't anything near that standard of recognition playing for us now. Even Given would be down the list a bit for goalkeepers, maybe if he had saved two of those penalties against Spain, who knows.
I don't know why Keane only seriously registered for one year, Man U had plenty of TV exposure.
And yes Don Givens? I think he got the Soviet's vote.