I do. I have a scupper pro.  In short:

What the Polespeary Whispererrer said..,

Spearfishing using a kayak is choice. I've used a variety of SOT kayaks for spearfishing. You can make it as simple or as complicated as you want in terms of set up - which is part of the fun.

I pretty much don't use an anchor at all now - don't even pack one. I paddle to a likely spot then clip off a 10m rope floatline by stainless steel snap lock to the bow and clip off the other end to my weight belt keeper and tow the yak when hunting. Can tow with a couple of fingers it's that light on the water. If an interesting area is uncovered I either clip off my floatline to some kelp stalks or anchor it under a rock then hunt freely using my reel gun

Everything gets clipped off or stowed when using a kayak. Great option for exploring new areas and increases your range. Very productive weapon of choice

How do you find it diving off a kayak in high current areas or more than 1/2m swell?  Just for curiosity sake

Haven't been out in big swell- usually means the diving is cr@p anyway in terms of snapper. Is fine in 30 knots and a wind chop but have not tried in an area with much fetch. Much over 30 knots and it is very hard to paddle these tugs in a strong head wind.
Stability is not an issue I think the barges used by fat fishos are prolly too wide, hence slower. Still, you don't usually have to go far, so you can have a good time on most yaks.
Gearing up and getting on/off are really simple technique. I did it with no experience and it was just totally cool and fun.

Always wear the long johns. A short paddle (1 km or so) is ok in a suit, but if going some distance I put my suit jacket on before I get in the water. It is much easier to paddle without a wetsuit on. Wear a rash vest and a wind and waterproof shell on the way, or a thermal top in mid winter. Do tie stuff on to the boat before getting into your suit just in case you tip over.

Big shark clip from a yak line to big kelp base used to work for me to anchor my old prowler 15. I used to have a bin that fitted snuggly in the back (bungeed down) that id throw the catch and floatline in. For v short paddles id wear my suit. For really long ones id load the nose of the boat with weight belt suit fins etc and get changed on shore when i got there. Rudders are a must down in welly with the wind! Take heaps of fresh water to drink...yak spearing is thirsty work! Hardest part i reckon is putting fins on on the yak when shore landing aint an option.

Aint no one to annoy on a yak mate...im a bit unco so putting long fins on in deep water is harder for me than whacking em on above the briney.

How hard is it to fit your dive jacket then? Could be quite a balancing trick I would thought, I struggle standing on land at times

Everything gets "clipped off or stowed".  Good idea to stow your wetsuit jacket, fins and weight belt in one of the hatches if possible.  Flipped my kayak first mission out on the first wave, that's when I invented the rule!  Run bungee or cord across the deck to clip your belt off or tuck fins under while kitting up.  You get in the habit of doing this

Spearos need storage space - and most plastic SOT fishing platforms have TAC (Tackle Acquisition Syndrome) - way too much stuff on board that isn't necessary for us.  What we need are large storage hatches and the ability to clip off gear.  The more I look at the plastic fishing SOTs available, the more I come to the conclusion that shorter, simplier is better.  If you want paddling performance for big missions (and kick-ass hull design) you'd spend the dollars on fibreglass

As for rough water, most spearos aren't targeting open water spots and are looking for protected calmer patches (lee of islands etc).  We are blessed in NZ with plenty of coast line and tend not to have to work open water reef systems.  Remember, plastic fishing SOTs - Viking, Ocean, Mission are NZ manufacturers (length 3-4.7m, beam 70-80cm, weight 25-35kg+, with most 30kg+) are designed to be stable for guys up to 120kg+ while sitting in open water fishing (how boring).  Barracuda do an exceptionally light plastic at 18kg, 4m length and $3k.  Viking and Ocean both offer Fish Pods (insulated), with the Viking Pod most likely to work as a converted fish plat.  Most fish storage will be in the rear well behind the paddler (this is where an optional pod might fit), you can buy insulated fish covers if your not in the market for a pod.  Advantage of a pod converted to Plat (I've converted my Perception Swing Kayak Pod to a Plat - 6 years and still kicking) is you can anchor up and use your plat - plus keeps your kayak and gear clean from fish goo

If you go a fibreglass fishing surf-ski (SA manufacturers include Stealth, Pinnacle, Kaskazi, there are OZ manufacturers, but mostly surf-ski design only) your talking highly aesthetically appealing hull designs, internal fish bins (potentially great for gun, fin and wetsuit storage), bigger dollars (3-4k+) and importing, but much better paddling and ocean performance (longer hull length 4.3-5.7m, narrower beam 60cm, lighter 18-26kg) - downside is lack of hatches (may require customisation), not able to kit up on board due to narrow beam, and the need to anchor or stow on the beach - fibreglass is tender around rocks and more than likely won't handle big impacts like plastic.  So you may have to consider kitting up in the water.  Just ask Bounty Hunter about that.  I have fond memories of being chased back to our kayaks by a big hungry bronzie that Marcus had feed a blue moki to involuntarily.  He had to unkit in the water next to his kayak, I sat my precious bottom in the kayak and hugged plastic

As TSW said, you typically are wearing your wetsuit pants and I'd add your booties (with dive knife always at the ready).  Most SOT fishing kayaks have a wide beam (70-80cm) which is really stable for kitting up while sitting in the kayak.  If you are concerned, you can put the legs either side in the water, or sit sideways in the seat with both feet in the water.  Use sea water to "lube" up the wetsuit jacket and put on, take your time and don't panic. Tight fitting suits don't work well, so if you can cut back on the pies all the better.