The problem with your theory here is that unlike many guys at the age of 29, Horford is ALREADY showing significant signs of decline.
Objectively:
* His Per 36 scoring numbers are the lowest since 2012/13
* His per 36 rebounding numbers and REB% are the lowest of his career
* His FG% is the lowest since his rookie year
* His Free Throw Rate is the lowest of his career
On his per 36 scoring: Horford's USG% was the lowest this year in the past 4 seasons as ATL has moved the scoring load over to Milsap and Teague. Whether that is due to a decline in Horford or an ascension of Millsap or simply reflecting team long-term goals is debatable. Millsap is actually older, but under long term contract.
On his rebounding: Most of Horford's rebounding drop is from the offensive end, where he's grabbing fewer ORBs because he's taking more 3PT shots (his 3PAr was WAY higher this year than any prior season) and setting more high screens for Teague, and thus playing farther away from the basket. He also has a slight drop on the DRB side because Millsap usually takes post defense and Horford tends to be the high-paint defender and the guy assigned to the opposing 'stretch' big.
On his FG%: Again, this is a symptom of the increase in 3PAr. Increasing 3PT attempts will tend to reduce FG%. However, Horford's eFG% (.547) was above his career average (.543) and his TS% (.565) was still very good and only slightly below his career average (.570). I.E. - he is still a very efficient scorer. Amir was our only player with a higher TS% than Horford (and largely because Amir took comparatively far more of his shots in close to the hoop).
On his FTAr: Again, taking more outside shots will tend to reduce the number of FTA that a player gets.
These trends are part of the price of Horford transforming his game into more of a 'stretch big' who can hit the 3PT shot.
I'm not going to necessarily assert that signing Horford to a max deal is necessarily, "the answer". I think the answer is more subtle and depends on multiple factors.
But I don't take those particular numbers as any clear indication of decline in Horford's game. I think the numbers you cited are really just symptoms of a strategic _change_ in his game.
Horford's various 'advanced stat' metrics all stayed pretty solid, posting PER, WS, WS/48, BPM & VORP numbers well above his career averages.