We were using parachutes for the Space Shuttle SRBs, but there are certain important distinctions - the SRBs were, to a first approximation, "big dumb pipes", and had much less of a problem with saltwater damage due to water landing needed to cushion the impact. There were 3 parachutes, for a total of 3x 990kg [1] for the SRB's empty mass of 91'000kg. While Falcon Heavy's first stage is lighter (25'600 kg empty, each [2]), you would need disproportionately larger parachute size to achieve soft landing on the ground as opposed to SRB's water landing, to avoid salt water damage. And to possibly handle passenger flights.

Off of the top of my head, with parachute landing you add mass because both:

- the large parachutes are quite heavy themselves as above (add some overhead for covers and support installation; I can't find any numbers)

- needs increased structural integrity to handle the tug during deployment and the much faster touch-down on landing; with propulsive landing you can essentially touchdown at 0/0/0 vertical/horizontal/angular velocities, as soon as you nail down the math of flight characteristics and engine control

- possibly some sort of reaction control, to achieve proper deployment attitude

- probably a smaller drogue chute(s) to handle supersonic flight, with all the complexity it adds

Moreover, using chutes:

- completely prevents RTL flights

- complicates abort modes; you'd need to dump fuel and oxidizer quick (without mixing and igniting, good luck) to be able to rely on the chutes alone.

However I guess the overriding concern for Musk was quick turn-around. With a parachute landing you have less control over the touchdown point [3]; the logistics of recovery, refurbishment and relaunch become much more involved, possibly spanning an ocean [4]. And with longer turn-around you need more flight hardware, and more ground support, to handle given amount of orbital or surface-to-surface traffic. Call it reducing the capex by going for somewhat costlier option that ensures much higher flight hardware utilization.

Lastly, using parachutes would create an image of low reliability; it's not something we would consider as to be routinely performed by commercial passenger flights. You don't want to ship passengers to "somewhere near your destination"; you want to deliver them to the airport, right next to the jet bridge (call it rocket bridge?) and promptly usher them to the passenger terminal.

Yes, yes, the routine BFR passenger travel is coming.

[1] https://en.wikipedia.org/wiki/Space_Shuttle_Solid_Rocket_Boo...

[2] http://www.spaceflight101.net/falcon-9-v11.html

[3] Gemini-style Rogalo wing would help, if it could be scaled. See https://i.pinimg.com/564x/b0/84/87/b08487e18f16402e4867981ff... and https://vintagespace.files.wordpress.com/2011/12/rogallo-win... Not as preposterous as it may seem, given that Buran's side-boosters were to glide to landing on deployable wings; see http://www.buran.ru/images/jpg/gk175-5.jpg

[4] you could bulk up the 1st stage enough to let it coast suborbitally all the way around globe to RTL, but that's another matter - and again uses up valuable fuel, and you run up against the rocket equation pretty quickly.