Baal predators aren't shooty?
Veteran Assault Squads with three storm bolters and a pair of meltaguns aren't shooty?
A swarm of attack bikes armed with tank-destroying multimeltas aren't shooty?
The thing is, there's more than one kind of shooting army. You don't have to line up four feet away and plink things with lascannons to be a shooty army.
The Blood Angels army list makes a fantastic 'Run and Gun' list. We have a lot of highly mobile, heavily armed units that have the speed to get into close range and lay out a blanket of lethal firepower and the strength to either initiate or defend against assaults should they come up.
While the blood angels are a very assault themed army, Assault is only half of our strength. You could tool up a VAS for assault, with power weapons and assault weapons, or you can load them down with plasma guns and bolters and make them a rapid-fire hit and run squad. You can put two plasma pistols and two plasma guns into an honour guard and make a highly mobile 5 man squad that can unleash 6 S7 AP2 shots at 12" or less and still be able to put up a good assault for a unit their size.
Meanwhile, just because you're geared for mobile shooting doesn't mean you can't also include a strong assault force, and few assault forces are stronger than a large Death Company. In fact, the presence of the Death Company actually means you can afford to invest *less* in assault units, since you already have a strong assault core.
You just have to look at the army list and its potential, rather than a one-sided stereotype of 'BA = Assault' and make a balanced list that includes a strong assault element but includes enough mobile firepower to take on the kind of tank-heavy armies that make so much trouble for assault forces.
One could argue that if you want to play a totally one-sided army of bright red, raving-mad assault forces with no meaningful firepower you should play World Eaters instead of Blood Angels.
BA are better at assault than regular marines, but there are forces out there that are better at assaulting than us (chaos, nids, Grey Knights) but there are few fporces that have good assault *and* as good of firepower as us.