You may have better luck at it that I typically have (read when my faction constantly are at war for decades at end with most of the time at war with 2-3 kingdomes you get the idea why its not ideal).
I might have better luck if I can engineer a situation where I have a safe corner, such as the Aserai lands, to be a part of or rule since I find wars are far rarer and tamer if your country has a good position. At any rate, I expect to have to shut them down if I want to join, say the Northern or Southern Empire, and wait until I or they have the northeast/southeast secure before setting them back up.
Then again, I remember, last December, playing for Battania before breaking away being gentler than I read about so I have no idea what the real normal is. Maybe people's kingdoms being at constant war isn't the norm but happens often enough to be complained about. I didn't have that problem last time until I had conquered 1/3rd of the constant since, at that point, everybody who could declared war on me as if I tripped over an invisible threshold.
About the workshop.
From my experience if I'm neutral the workshop will in most cases be standing after the siege is over.
However on rare occasions they have been "destroyed" or whatever you want to call it by the "sacking" of the kingdome(there was some message, but I never paid mind to it, and the workshop was gone from my listed).
Thank you for the clarification. I'll have to make sure I don't leave a lot of uncollected stuff in the Warehouses since I assume they'll be gone if my properties get sacked by the victorious army. I've made a habit of building my workshops in Vlandia since Galend, Jaculan, Ocs Hall, etc. are very safe cities as far as war is concerned and Warehouses let me dump whatever they need into their pockets so they don't need to rely on local resources. Combined with shutting down the competition, I'm averaging 700-1,200 per monopoly per day (I have 3 Velvets but they're making half to one third as much as the single Oil Press and Pottery Shop, indicating I'd probably make more passive income if I shut 1 or 2 of my Velvet Dyeworks down) so I'm now a multi-millionaire with as much money (and more passive income) then I had when I was a monarch ruling half the continent lol. I have screenshots I took over my past 1.5 playthroughs which shows how well I'm presently doing as a mercantile-focused character, so I feel like I finally figured out Workshops in Bannerlord.
Overall imo the "profit margins" from the workshops and caravans is pretty weak in the game, and is imo missing maybe even as high as a 0(but may not, should be dialed up maybe 1,5 x of what it typically is, or rather in some cultures - read pretty sure that in rl that a worker in China dont get the same pay pr hrs as they do say in a similar job here in Norway.) (Labor cost isnt reflected well in the game imo)(which makes makeing profitable shops in some of the factions harder than it should be - read if they are up for a long time, and the size of the town explode, the profit margins will typically be reflected by it, then you also have some issues with the resource lacking in some cultures or "too much of the same, so it leads too to much competiton".
That depends on your patience. At the moment, I agree with you if your intent in Workshops/Caravans is as a supplement to sustaining a professional army like in Warband, because you'll make practically nothing from Workshops and barely enough to cover daily costs with Caravans, but if you dominate the markets so you're the sole product maker (or have no more than 1-2 shops competition, globally) you'll make insane amounts of money (not as insane as smithing, of course, but comparable to winning battles as a warlord/monarch without the risks) and can casually throw cash around after a few years.
I'm tempted to lay low and wait for my 4 kids to grow up so I can send my daughters off running caravans while my son and his bride-to-be get busy making grandkids lol. I may do that if getting Eveything Has a Price takes that long since I love the idea of buying my way to power and prestige.
It's gratifying to be wealthier as a merchant prince than I was as a sultan ruling the entire continent lol. At the moment, my 5 Workshops are producing over 3,000 per day on average (3 Velvets averaging ~350 per day while the Oil averages ~900 and the Pottery ~700) while 6 Caravans average 500 per each or 3,000 per day (usually at least one of them has a bad day but it can spike up, now and then, leading to insane profits both per individual caravan and in total) for a gross average income of 6,000 per day by year 1092.
However, I do think average profits for Workshops in particular could use a boost--maybe by a factor of 2 so that 100-200 per day is the bare minimum passive income you can expect and 1000+ if you're doing what I'm doing.
if they ever added a campaign multiplayer id love to play with you.you can monopolise the market while i war monger the world 
