This is so true it hurts. The last dominant pass rusher we had was John Abraham. In 2012, and to your point he was a free agent near the end of his career. 

In the 2000’s these are the pass rushers drafted by the Falcons and the amount of career sacks they had 
Name/Year drafted/career sacks 
Randy Garner (01) 0 sacks 
Ronald Flemons (01) .5 sacks 
Waine Bacon (03) 0 sacks 
Demetrin Veal (03) 0 sacks 
Chauncey Davis (05) 10 sacks 
Jamaal Anderson (07) 4.5 sacks 
Kroy Biermann (08) 23.5 sacks 
Lawerence Sidbury (09) 5 sacks 
Cliff Matthews (11) 0 sacks 
Jonathan Massaquoi (12) 6 sacks 
Malliciah Goodman (13) 0 sacks 
Stansley Maponga (13) 1 sack 
Vic Beasley (15) 37.5 sacks 
Takk McKinley (17) 17.5 sacks 
John Cominsky (19) 1.5 sacks 
Ade Ogundeji (21) 3 sacks 
Arnold Ebiketie (22) 8.5 sacks 
Zach Harrison (23) 4 sacks 
Bralen Trice (24) 0 sacks