Not quite. The problem with the "there are already laws to take care of it" argument is the enforcement problem.
That's one of the reasons that legislatures will often pass apparently redundant laws that re-criminalize existing criminal behavior. ("Anyone jaywalking while carrying a concealed tuna fish shall be guilty of a class B misdimeanor.") The problem is that, while jaywalking is already illegal, evidently there's enough jaywalking-with-tuna to create a perceived problem and existing law enforcement (or prosecution) isn't doing anything about it.
Passing a new law, even a redundant one, can improve the situation in several ways. First, it makes it clear to the relevant agencies that the legislature considers this to be a problem (and therefore provides incentive to enforce the old laws as well as the new). Second, it raises the level of punishment and therefore the level of deterrence -- if I get busted mid-street with my pet tuna now, I get two fines, one for jaywalking and one for jaywalking-with-tuna. Third, it raises public consciousness of the issue and helps (e.g.) the local newspapers hold the local cops' feet to the fire, as it were (Daily Planet Headline : "Why Is Commissioner Gordon Sleeping with "the Fish Law?") Fourth, it makes it clear to the court that the existing jaywalking law is still valid and important, and it's less likely to be ignored as anachronistic or irrelevant.