The primary work product of a law firm is legal work, which the lawyers do directly. This is not a high-capitalization job: it's possible to be a Starbucks lawyer (or Lincoln lawyer lol) and not even have an office. It has this in common with the professional trades, like plumbers, electricians, etc.
Contrast that with a baker, who needs a workplace and significant capital infrastructure for mixers, ovens, cooling racks, trucks, packaging, inventory, etc. That's where the capitalist enters the picture.
If someone gave a law firm a cash infusion of $500,000, there isn't really a way to invest that into the business to get a payout. They can't buy better case files. There's no "litigation machine" that can litigate faster than ten lawyers. That's just not how that business works; it doesn't lend itself to capitalization.
It's true that many law firms have significant capitalizations, but they didn't get there overnight. They typically raise themselves on their bootstraps. Even then, the prestigious offices tend to be leased.