Which of these strategies do you choose:
a) Attach a parachute to the nose and let basic physics work.
b) Try to balance it atop rocket engines firing from the bottom.
I realize you were going for humor (and got it; congratulations on being moderated +5 Funny). But here's a serious answer.
It depends on what you are trying to accomplish:
If your top priority is to save the rocket stage, then you pursue an engineering strategy that has the best chance of saving the rocket booster. Maybe that means a parachute system; I don't know.
But a parachute system adds mass and complexity. It becomes another critical system ("if the parachute fails, we lose the rocket stage"). The rocket stage needs functioning rocket engines, so landing on the rocket engines is another use for those engines rather than a new system with a single purpose. All else being equal, the simpler design with fewer systems is more likely to succeed in its tasks.
If you add a few hundred kilograms of parachute system mass, that's going to mean the booster can push less mass to orbit. I'd guess that the loss factor is higher than 1... that each additional kilogram of non-fuel mass on the booster reduces the to-orbit capacity by more than one kilogram. But ask a physics expert for the actual numbers.
Note that new software to make the booster land on its engines does not add mass to the booster.
So I'd say that if your top priority is to efficiently deliver stuff to orbit, the parachute system is right out and the clear engineering decision is (b).