Such reasoning isn't very intimidating and therefore not as good for recruiting, as opposed to telling someone they'll burn in hell for eternity if you don't join us.
The name Jesus is derived from the phrase "god saves." Just thought I would throw that in.
The problem with other ideas doesn't hinge on recruiting. It hinges on two factors. One is that if there are other ways to heaven, Jesus's death was not necessary. The second is based on the whole reason for Christianity, namely Jesus rose from the dead.