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.
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.