2
♣ is already way too busy a bid, IMO.
Neither 2/1 nor Standard American specify a particular response structure to 2
♣ as "standard". Particularly since, like political parties in France, there are as many "definitions" of these systems as there are people playing them. That said, I'll grant that 2
♥ "double negative" is fairly common among 2/1 players. What if I have a different idea how to respond to 2
♣, one that's not compatible with your "stick the balanced 20-21 in there too" idea? Now I either have to abandon my preferred responses, or find another way to show the 20-21 hand. And as Zel says, there can be memory problems (although that's true of just about any setup).
For the record, I don't play Puppet Stayman. With those partners for whom basic Stayman is complicated enough (I seem to have quite a few of those) I play that. With those willing to take on a bit more (currently, unfortunately, none) I play Romex Stayman (over 2NT). If I'm bidding 1NT with a five card major, I just rebid as if it were four. Over 2NT, rebids after Romex Stayman will uncover the 5-3 fit, if there is one.
Opener's rebids after responder's 3
♣ Romex Stayman:
3NT: 4-4 in the majors
3
♠: 5 spades
3
♥: 4 or 5 hearts (now 3
♠ asks which it is)
3
♦: any other holding, so fewer than 4 hearts, and fewer than 5 spades (now 3
♥ asks if opener has 4 spades).
A Romex NT ladder:
12-16 HCP: open 1minor (usually), rebid 1NT
17-18 HCP: open 1minor (usually), rebid 2NT
19-20 HCP: open 1NT (artificial, F), rebid 2NT
21-22 HCP: open 2
♦ (artificial, F), rebid 2NT
23-24 HCP: open 2
♣ (artificial, F), rebid 2NT
25-26 HCP: open 2NT (natural, FG or — very rarely — 4m)
27-28 HCP: open 2
♦, jump in NT
29-30 HCP: open 2
♣, jump in NT
In the current "two card" version of Romex {at MPs, play "Romex" when vul, "Romex Forcing Club (RFC)" (basically a Precision variant) when not vul — at IMPs play RFC only at favorable} there are two ladders:
Romex:
12-16 HCP: open 1minor (usually), rebid 1NT
17-18 HCP: open 1minor (usually), rebid 2NT
19-20 HCP: open 1NT (artificial, F), rebid 2NT
21-22 HCP: open 2
♦ (artificial, F), rebid 2NT
23-24 HCP: open 2
♣ (artificial, F), rebid 2NT
25-26 HCP: open 2♣, rebid 2♥ (Kokish Relay)
27-28 HCP: open 2
♦, jump in NT
29-30 HCP: open 2
♣, jump in NT
RFC:
10-12 HCP: open 1NT (no five card majors here)
13-16 HCP: open 1
♦ (usually), rebid 1NT
17-20 HCP: open 1
♣, rebid 1NT (modified Stayman here, so that opener can show whether minimum (17-18) or maximum (19-20)
21-22 HCP: open 2
♦ (artificial, F), rebid 2NT
23-24 HCP: open 1
♣ (artificial, F), rebid 2NT
25-26 HCP: open 1
♣, rebid 2
♥ (Kokish Relay)
27-28 HCP: open 2
♦, jump in NT
I'm not saying any of these is somehow "best", just that they work for me - or would if I could find a partner willing to play Romex.