There are really aspects, offensive power, defensive power, utility being the branches
Chase provides offensive power and in some cases utility, so it is important. But it's not all there is to it.
For example, Hinata's two chase together actually don't do all that much damage, most people don't really care about the second chase actually and use her chase purely for the utility of acupuncture.
Hinata also have the defensive capability of her mystrey, making her an excellent tank.
Sage Naruto, on the other hand, is your bruiser. He is fairly tanky, in fact almost as tanky as hinata w/o mystery. He generates a pretty tanky clone, one that's almost as tanky as some of the more fragile characters you can field. Should the clone be alive, his standard attack is guaranteed to hit AND, should the enemy not be immune to low float etc, guaranteed to cause low float and, with correct team configuration, a chase chain. Turn 1 chase chain is awesome. His mystery hits like a truck, enables high combo chase and is AoE. Finally, he provide 20 extra chakra for your team (and the fact that it is before he acts as opposed to begin of round is important, as this DOES allow you to use 120 on turn 5, should you need it)
Tanks have the best utility in PvE, where the enemy is known, predictable and *. You can easily gimmick pass much stronger AI mobs using hinata. The prime example being she is in MANY ninja exam formation, tanks are also good in survival. As far as live PvP is concerned, hinata is more used for her acupuncture than her tankiness, because mystery can reach around her.
Bruiser, on the other hand, are more straight forward. You always need at least something to the effect, either by direct damage or by DoT. Otherwise, frankly you won't get anywhere. The capability of a bruiser are often dependent on its raw strength(different character gains stat at different rate) and the power of their mystrey.
Long chase chain really doesn't provide all that much benefit on its own, other than for hanzo SA. the actual damage of the chase depends on the raw power of each link, some ninja like tobi packs more punch in one chase than sasuke's 3. Generally speaking, other than utility effect like hinata's acupuncture, tobi's ignite etc, what chase a ninja have is fairly unimportant, as long as you can string them all together so they c*l be used fairly consistently every round. With the exception of tobi(which is rumored to be nerfed eventually on this aspect), as long as this consistency is achieved, amount of damage you gain or lose from chase chain is fairly minimal and not at all based on the length of the chain--tank and healers deal very little on chase, it's only the bruisers that matter as far as damage goes. Quite frankly, except fire against wind, no chase can one-chain-kill a target on an opponent of similar strength anyway, so having utility in your chase to disrupt enemy game plan is a far better idea. Ideally, your chase will interrupt enemy mystery, if not that, a stun or paralyze to halt enemy chase chain (thou if it's stun, why not just interrupt the mystery unless enemy is earth/lightning which can immune it) or at the very least, a bit of ignite so they can't heal.