The invisibility isn't cowardice, but merely a tool for his jests. Many champions have it, and the only cowardly one I can think of would be twitch. All the others are designed for the purpose of utilizing it to get an otherwise-immobile champ (except for Vayne and potentially Kha) into a fight. This doesn't save him from AOE, CC, being blown up like any other squishy, and having a slower combo than most unless he's merely topping someone off with an quick q, e combo. If they are low enough to die in an instant, they either fed shaco too much or shouldn't have been there without wards. The free flash w/ invis is not nearly worth potentially a quad-dash with 3x the damage, twice the cc (potentially four times), and an invis-clone if she gets low. Shaco is no where near that slippery unless he generally outplays his opponent by being unpredictable. Additionally, if he wants to sneak in to a fight, he effectively dooms himself unless he immediately ults after one auto and e. Even then, he's likely dead and he only gets a kill if he had a semi-low squishy to burst to begin with. His boxes are easily killed before they stealth by most champs, and if he pre-placed them than he, again, generally has to outplay an opponent or be smart to get them to hit them. It isn't cowardice, but strategy that ails you. Your strat of "go in. Kill clown." just doesn't get past a defensive fear and invis unless you have some true sight, cc, a team mate, or some other way to get to him. Keep in mind, he only gets that invis if he either didn't use it going in or managed to survive its CD (a notable feat pre-40% CDR in a teamfight).
His clone only does 1k damage if he's AP, and even then he must first fool you with it. If you got hit, he either played it right or you played it wrong (usually both to some extent) and you fell for his trick. The super shot invulnerability when ulting is only enough to dodge one thing if he times it perfectly. Everything about him is either "outplay opponent using actual strats" or "use slipperiness to run all the time and be a useless, last-hitting (maybe) troll to your own team."
You may hate him, as many do, but is it because he's cheap, or because you couldn't outplay him? You know it's more than possible. One pink or red trinket and you know where he is when he goes invis to try and run, as well as where he places a box. Seeing his clone take bonus damage from things lets you know which one is real. Not staying in lane low early keeps him from getting kills (like any other assassin), and his invulnerability is annoying every 60 seconds or so (shorter later in game), but if you want slippery, try fizz's trollpoll, or LB, or maybe a little bit of peel if you want to force enemies back instead of running away. Either way, Shaco isn't cowardly unless he's low (and runs like any normal person should unless they know a kill is there to get) or he's bad/new (self-explanatory). He just uses a little more tact than most, opting to surprise an enemy rather than charge in like Garen/Riven/Talon/etc and fight a fair 1v1. Shaco's kit isn't the strongest in instances like that unless he got a few early kills. He shines when he can outplay people and survive, or when he can assassinate. An argument could be made that ALL assassin's are cowardly, but then you have to consider that the good assassins aren't really once they can kill. They just know when to do what.
Also, if you can manage to jump into a fight with every champ, you are a god. W/o flash, I've yet to see very many Annies, Tarics, Ashes, Varuses (Varusi?), or other non-mobile people (like teemo) do it. Usually they're too busy being back-line pansies to go in (like they are supposed to) while the people who are supposed to go in do their jobs (like Shaco). You can argue cowardly all you please, but if you lose to a Shaco and you weren't low before the fight started or he wasn't fed from allies, than you more than likely got outplayed (kinda like you would against a lot of champs with any mechanics),