The problem with slow walkers IMO as we've seen in The Walking Dead by season 3 is individuals even without a gun are able to take them down easily. Andrea for example by season 3 is able to fight off three zombies with a simple pocket knife and take them down.
In order for us to suspend our disbelief and belielve that the whole world has gone to shit with slow walkers becomes more difficult based on individual's skills at killing them.
Not entirely. It would be another matter if EVERYONE on the show had come into the zombie apocalypse already possessing the skills necessary to kill zombies without much effort, but that's not the case here. For example, Andrea was lucky the time she killed the zombie in the camper with a screwdriver. She couldn't shoot a zombie in the head until mid-2nd season. Over time, she has honed her skills. Some like Rick, Shane and Daryl already had experience through hunting or police work. Others were into protecting their own homes. As for the rest? These people have spent what.... a year, almost two in this mess? It's not that hard to believe these people know how to kill zombies with relative ease by now.
Contrarywise, you've got a lot of secondary characters (*cough* REDSHIRTS! *cough*) which our heroes have come across who still aren't that adept at self-defense. There are many in Woodbury right now who clearly have been living there pretty much the entire time and haven't made any real attempt to develop those skills. They have the misguided perception they don't need these skills because there's always going to be someone else around who can do those things for them, thus they absolutely suck when it comes to accuracy with a bow or a gun. Then there's side characters like the hitchhiker a couple of episodes ago. These are people who'd probably shit their pants and become lunchmeat before being able to stab a zombie with enough force to penetrate/destroy the brain.
Setting aside for the moment the idea that suspension of disbelief is thrown out the window upon the first mention of the word "zombie," survival and adaptation are at play here. In these types of stories, when the world goes to shit, it's rough and chaotic assuredly, but if someone goes through enough and learns how to survive along the way, you bet they're gonna make it look easy. This will never fully exempt them from eventually getting snuffed out, but at least they have what they need to give themselves a fighting chance.
As for the argument of slow vs. fast walkers as it is relevant to The Walking Dead
, the conceit there is that you'd need the zombies to be slow regardless of whether or not it makes the most sense, because the show would be over really quick. With slow zombies, yes they are easier to evade, but the IDEA of them... their lingering presence... is what helps keep the chase equally compelling (for us) and terrifying (for the show's remaining living characters). They might not be breaking your doors down (unless there's a horde of them), but they're always there.