Of course lieutenant and mayor would be able to see the job or at least limited number of them. Lieutenant would see how many police, medics, firefighters, and road crew are available, while mayor would see all government jobs, so this excludes taxi driver and delivery at this time. Since those are privately held jobs not paid by city funds.
But if someone had broken legs, you say that they'd never get the help they need because they can't see if there's a medic? I'm sorry but that is total BS, considering that if someone like that is in need, they could either stop an officer or get a ride from a taxi, or by some other means find their way to the hospital, since generally speaking people just drive them self there and never call the medic as it is, which is why the job IS so boring. Some jobs such as medic/firefighter/SWAT may not have much to do and could be considered boring, but not all of RP is ever glamorous, if you think this is simply another gamemode to shoot people down, you are sorely mistaken. However if you have any useful suggestions how to make them more useful and have it so more people would be willing to do it, which doesn't include hiking their pay higher because that just makes people take it for the money that they get for doing nothing. As the saying goes, "it takes a village" meaning all parts must work together in a cohesive group for the city to do well. I'm sure if you or a friend had broken legs you would easily find your way to hospital, and since in the new map, the hospital will be actually inside the city limits, it is far more accessible than it is now, so while it may be a pain for a lil while if that's what you're concerned about it, soon as we switch over, it'll be in a far easier location to reach.