The kit you are recommending would take up a lot of space, but is a great list for vehicle-based trips for someone who has at least some basic training as you said. Some of the items on the list are a little overkill (pun intended) for most layperson FAKs:
> sam splint
https://www.rescue-essentials.com/sam-splint-original-36/
These are nice, but splints are pretty easy to improvise.
> chest seal
https://www.rescue-essentials.com/hyfin-vent-chest-seal-twin-pack/
Most could skip this as it would probably never be used. In its place I would have some duct tape.
Or the compact chest seal twin pack to save some space.
> z fold quick clot
https://www.rescue-essentials.com/quikclot-combat-gauze-z-folded-military/
12 feet of quick clot is a lot for non-military IMO. There are smaller packages of the z-clot that you can combine with the coflex or just go with an Israeli bandage.
> and one of these
https://www.rescue-essentials.com/advanced-medications-module/
Meds go bad and I usually go with smaller quantities than this awesome monster module.
Make sure to have an Epipen or two on hand if anybody has severe allergies.
Taliv, what would you bring in a minimalist FAK for side trips to go in a small daybag? Presume two people.
it does take up some room. but it seems reasonably prudent if you're going to be wheeling as far away from hospitals as we tend to get. I pack all that and more into a bag that's about 14"x9"x6".
splints are easy to improvise in some places, especially wooded areas. but on the plains or beach, maybe less so. and if you are going to improvise, make sure you carry lots of wrap or paracord or something.
I shot competitively, mostly sniper style matches and 3gun. being around 200 dudes running and gunning in a remote location means my kit has a lot more trauma stuff like chest seals and tourniquet and QC than your average kit. but hey, you can fall and impale yourself pretty easy, especially on a bike. or using axe or chainsaws. or getting gnawed on by bears. not following safety rules during a recovery, etc....
the awesome monster module gets split between lots of kits. i have small kits in each of my backpacks. in my trailer. in my truck. etc. it's prob way cheaper to buy bulk bottles of each at sams club or something, and then put them in little pill baggies. but it's nice having meds labeled and in factory packaging if you get searched in an airport or crossing a border or something.
epipen is great idea. i would have one even though i'm not alergic but for some reason, they're like a bazillion dollars these days.
i think when you're putting together your kit for little trips, you should tailor it to your specific circumstances since size and weight may be more of a factor. start with the big kit and then see what you feel like taking out. is it summer? winter? is hot or cold exposure a potential issue? if you're exploring mountains in winter, you can prob leave the bug bite stuff at home. but take extra chapstick, etc. your side trip involve eating street food? bring the stomach meds. always bring some booboo stuff and antibiotic ointment.
tbh, I'd bet most of the things that distract from an adventure are things like dehydration, sunburn, altitude sickness, cold/flu, upset stomach, etc. so it really depends a lot on the willingness of your companions to suffer through that. traveling with wife and kids? or a bunch of "it's just a flesh wound" veterans?
