Coming from someone who loves the Splatling class of weapons, here are my thoughts.
Playstyle - This is a defensive weapon class most accurately. Whereas it does have a high fire rate, long range, good turf coverage, and overall power, you need to charge up for each volley of shots. Because of this, you can't really go buck wild at the front lines. That's why I use my Splatlings in a defense/support role.
Purpose - The Splatlings, like most weapons, has myriad uses. But the ones that the Splatlings specialize in are in long ranged combat and control. Unless you are using the Mini Splatling, you don't want to get too close to your enemy. Take your engagements from a distance and use your range to bully other shorter ranged weapon holders into either keeping their distance or getting splatted, preferably with extreme prejudice.
Why would you pick one? - Versatility. As covered before, Splatlings are good at many things. Long ranged combat, control, turf coverage (which leads to increased mobility for you and your team), and intimidation factor. Being pressured by a Splatling is no fun and you aren't guaranteed a splat just by getting in close. This is another strength of the Splatling class in comparison to the Chargers, another weapon with a similar playstyle. Chargers struggle in close quarters combat because they need that charge to be truly deadly, meaning that other weapons can get a number of shots (or swings depending on the weapon) before they can charge. I know what you're thinking, and yes they can use quick, uncharged shots to get the job done. But that method is a little unreliable in many CQC situations. With a Splatling, a small charge can give you a nice 10-12 shot burst. Plenty to get the job done considering that it is a 4-shot kill weapon! But that isn't the Splatling's strength so don't go running into battle all guns blazing! It is simply a point to consider when picking a weapon.
Are they viable? - I would argue yes. The only real downside to the Splatlings is the charge time. It can lead to rather bad situations at times, but so can the slow fire rate of the .96 Gal or the short range of the Dapple Dualies. Most weapons/weapon classes have their strengths and weaknesses and you should pick your weapons accordingly. Does this weapon appeal to me? Do its strengths play to my preferred style? Are its weaknesses something that I can overcome? In my case the strengths of the weapon outweigh the weaknesses by a significant margin. Even having to charge my shots is something that I can dig as I am a slower, more methodical player. This weapon suits me to a T! But that is straying on a tangent. The Splatlings are plenty viable but may take some practice to make the best use out of them.
Did I list too many questions? - Are bananas purple? Before the paint, of course. :p
I would get into how Splatlings compare to other long range control methods, but I think GreenSpiny's comparisons are spot on. The last thing to talk about is which Splatling to take into which situation. The base heavy is good for extreme long ranged pressure thanks to the Sting Ray special which allows it to compete with Chargers more effectively and comes with the Sprinkler which is good for additional coverage, charging your special, and creating temporary choke points. The Heavy Splatling Deco (or the Fabulous Splatling) instead has the Bubble Blower which is great for coverage and for smoking out your enemies from cover. They also act as floating Splash Walls so make use of that as much as possible! Speaking of Splash Walls, the Deco has those. Use them to give yourself some breathing room and to prevent potential advances. That combination of sub and special make the HSD a bigger threat in close quarters. In my already long winded opinion, I would use the original on maps like Moray Towers where you are likely to encounter other long ranged threats but I would switch to the Fabulous for maps that have a leaning towards CQC like Port Mackerel or the Manta Maria.
I think that about covers it. Thanks for your patience! This got longer than I intended for it to.