I took a quick look at who would've got the 2 spots if the rule had been applied for this year's CL. Using the Club Coefficients at the end of the 20/21 season, these are the highest teams that didn't qualify for the CL, along with their respective league positions and how many teams from their league qualified for the CL:
Arsenal (8th, 4 qualified)
Roma (7th, 4 qualified)
Spurs (7th, 4 qualified)
Lyon (4th, 3 qualified)
Napoli (5th, 4 qualified)
Bayer Leverkusen (6th, 4 qualified)
Basel (2nd, 1 qualified)
Now, under the rules, Arsenal, Roma and Spurs would not get spots because that would require them to leapfrog teams that finished above them in the league (Leicester and West Ham for Arsenal/Spurs, Napoli and Lazio for Roma). Thus Lyon and Napoli would get the 2 'historically successful'' spots.
(Note, however that the CL is expanding by 4 spots and its thought that France would get 1 more automatic spot for their 4ht place team, so Lyon would probably qualify by league position under the new rules. If that was the case, the other 'historically successful' spot would of the Basel, since Leverkusen can't leapfrog Frankfurt who finished 5th).