Both this and the other examples I describe as coordination, not abuses, tactics and teamwork, not abuses.
Not sure at all why they would be seen as abusive- shoving down an enemy at the feet of your ally, sleeping foes so your ally can hit them or ignore them and go after others?
With cyclical initiative, you have foreknowledge of the order of actions, thus you can abuse it. With non-cyclical, you can try to do tactics, but because of the randomness of the rolls, it won't always work out as you plan.
Cyclical Initiative:
Round 2: (now the order of initiative is known)
1. PC A
2. PC B
3. Monster
4. PC C
PC A decides to shove Monster to knock prone, knowing PC B will get to attack with advantage. Player B attacks and then the Monster gets up and attacks. PC C,
knowing PCs A and B will go before the monster next round, likes how the shove worked and uses his attack to shove instead of dealing damage. On the next round, PCs A and B will
both get to attack with advantage.
Non-cyclical Initiative:
Round 2: (same as above, but no one knows for certain what the order will be
next round)
1. PC A
2. PC B
3. Monster
4. PC C
Same strategy but PC A shoves (hoping either PC B or C might go before the monster, they don't
know) , PC B attacks with advantage, Monster goes, PC C shoves instead of dealing damage.
Round 3: (oh, look! a new order... no one
knows who is going when! how exciting!

)
1. Monster
2. PC C
3. PC A
4. PC B
Oops! The monster goes first and gets up, attacking PC C and rolls a critical, PC C is dead! Boo-hoo!

PCs A and B weep over their fallen comrade, attacking wildly and hoping to avenge the death of PC C.
So, yeah... there is a definite advantage to using a cyclical system that players (and the DM LOL) can exploit. The inherent randomness of re-rolling every round doesn't make teamwork and such impossible, but makes it more challenging.
We define abuse very differently you and i.
Yeah, I would certainly say we do!