For both sentimental and other reasons the family business is not sold (i.e. may have never had audited financials since it had a single owner and no outside investors so it would be near impossible to sell it for a price the family believes is fair).
These type of "family offices" don't have any full-time investment management staff. They work with the same type of advisors an individual who had $5M of investment assets would.
Also, it’s possible to determine a value for any company.. not sure why you think it isn’t? Net profit/compensation to owner multiplied by a multiple determined by what industry/sector it is in is how small business valuation is done, plus/minus assets/liabilities.
Second issue on valuation, logically you're totally correct. In a jointly owned family business logic and Excel aren't the only way the business gets evaluated. Depending on the structure a sale may even be blocked by a minority owner member so all parties have to agree it is a fair sale price to sell.
If this "family business" has built up $5-10M in investment assets and the operating business runs at a break even while the investments generate $1-3M a year in gains is it a small "family office" or a struggling family business with an excellent treasury team managing the investment assets?
https://en.wikipedia.org/wiki/Family_office
But I think you're right as well.
When your networth is high enough such that paying for a professional money management means you get to recoup back the time you otherwise would have to spend to do so.
Family offices often deals with more than just finances, but also things like butler/chauffeur and other utilities (like gardening etc), and if they are truly rich, they would provide a fixer type service (e.g., somebody to get you what you want - like if you wanted a yacht/mansion/luxury goods, they'd be the one doing the looking and present to you the good options without you having to sweat).
The tl;dr seems to be "when it saves you time/effort," vs. "here is a financial threshold where a family office is more financially efficient than a traditional wealth manager." Right?
When does it make sense to have a family office? I would guess, when you want to employ at least one financial professional full time? Is that right?