Whether the player dies or not is not the point. It's about having the ink necessary to be able to maneuver more securely. The enemy team can easily disreguard the team that rushed and go around the center to fill areas that aren't inked, along with a special they have at the ready because they covered ground more. And... there's the problem with prioritizing speed over ink. The team that rushed won't have enough resources to fight (or fall) back with.
The team that rushed would be setting themselves up to something called a
flanking maneuver. Simply put, that's when one team has the enemy team attack forward while other groups (or players for Splatoon) would go and position themselves to an area that the enemy going forward would be more prone to defeat. An example of what I mean is this neat diagram of the Battle of Marathon, executing a maneuver called the double-envelopment.
Another example is the
pincer movement. It's similar to what I posted above, however instead of going for the enemy they can just go
around them. Here's an image for what I mean:
The team with more ink is able to pull these kind of techniques and more because they put themselves at less of a risk than the ones that quickly maneuver to a specific position.
Slow and steady wins the race. Splatoon makes good use of that idea. It's what makes this game a lot different from other shooters where speed is necessary to stay ahead of the competition.