In the 45 years I've been driving, most of which were on the poorly maintained streets of Hawaii, I've had only one flat that could not have been fixed by a plug kit (and even that one was my fault). So no, I don't consider a spare an absolute necessity.
Even in cars that did have a spare, I felt it was easier to use a plug kit than to change a tire (US spelling), so my spares really never got used.
Those slime/goo sealant kits are even easier to use, but I prefer plugs because if a single plug can seal the leak, it's fixed (and you can use more than one, but it's not considered a permanent repair). With the tire sealant goo you still need to have the tire repaired, and that stuff is nasty so some shops will charge extra when fixing a tire sealed with goo.
Another advantage of plugs is that they won't damage TPMS sensors. Some goo kits claim to be safe for TPMS, but if a sensor does get damaged it will add a lot to the cost of repair. And finally, plugs can fix larger holes than goo.
That being said, if you have driven on the tire while significantly under inflated, it should ALWAYS be inspected by a professional, even if a plug can seal it. Driving on a tire with low pressure can damage it, and it needs to be removed from the wheel and inspected.
So what about that one time I did need a spare? It was also flat, of course. I'm an "out of sight, out of mind" kinda guy, so while I'm pretty diligent about monitoring the condition of the tires ON my car, I tend to forget about the tire IN my car. Fortunately, since I carry a plug kit, I also carry a compact compressor, which I used to re-inflate the spare.
My latest car is a 3rd generation Mazda MX-5, which does not come with a spare (or even have room for one). It comes with Mazda's "Instant Mobility System" (IMS). Basically a can of sealant goo and a compact compressor. Oh, and that reminds me of the other thing I don't like about goo, it has an expiration date. I don't know what Mazda put in their sealant, but they also say that once you've used it, the tire needs to be replaced! WTF?!
I bought a Dynaplug kit, tested the OEM compressor to make sure it worked, and never looked back. Just remember to also carry some pliers or a multi-tool so that you can remove the offending object before plugging the hole.
Sorry for rambling on. So yes, I do consider a tire/tyre repair kit a viable replacement for a spare. No, it will not cover 100% of all situations you may encounter, but it will cover you probably 99% of the time (IMO). And since you have a spare already, you could leave it at home and call a family member or friend to bring it to you if you do get stranded.
As for me, since I don't have a spare, I just added roadside assistance to my insurance. But with my plug kit (and a portable jump starter) I'm pretty confident I won't need it.