A little harsh IMO... Tottenham amassed more points than any other club side in the top flight throughout the 60's.
https://www.myfootballfacts.com/england_footy/football-league/first_division_table_1960s/
It were difficult to win a title however great a team were and luck played it's part...You have to factor in, that in those days, that due to the two points for a win rather than the three meant that the final points tallies were often much more crunched up than they're nowadays. Long term injuries and all to often, more importantly, in game injuries, were major deciding factors on where points ended up. Substitutions were not introduced to the game until the 64/65 season or thereabouts ..
The Football league's hierarchies' idiocy at the time, actually introduced the one substitution ruling to the game - that a player could only be replaced due to injury, rather than tactically! I think they made the amendment to their nonsensical rule and tactical substitutions were made official in the 67-68 season..
There were also plenty of other good teams in those days and a club's wealth disparity with it's peers were less so and of lesser importance.. Clubs such as Wolves, Ipswich, Burnley, Leeds, Derby produced teams with innovated coaching.. There were also both the Manchester clubs, the emergence of Shankley's Liverpool, whilst Everton were also a powerhouse themselves, and then there were Arsenal towards the end of the decade...
You're right, we went close another couple of times and it were a shame Bill Nick didn't win more League titles and, Spurs be the first British club side to win the European Cup. However, the European Cup winners Cup and three FA Cup wins back then were no mean feats..
In those days under Bill Nick, when we got to a final, they may as well have handed our players the winner's medals and trophy, prior to kick-off as Nicholson and his team always found a way to win regardless of performance on the day. From what I've been told - bar the Cup Winners Cup final thrashing of Athletico Madrid where we turned it on, Bill Nick's three FA Cup wins , Two League Cups and the UEFA Cup win in 71-72 were all won with his team doing just enough to get over the line.
All the oldies and boomers share your frustration at only his one League title but I wouldn't call it an underachievement.. For me, Bill Nicholson were a winner.