I regard the Brooks saddle as a base to be custom fitted to your anatomy.
The leather used is vegetable tanned leather. The process makes it stiff by design. Think the old style shoe or boot soles
Chrome tanned leather is supple and it is used in upholstery, clothing and shoe uppers.
So two quite different leathers.

The vegetable tanned leather can be formed and then retain its shape. This is done by immersing in water, forming it and then letting it dry slowly.

Breaking in a Brooks-style saddle also uses your sit bone pressure to fine tune to your shape. The pressure comes from your weight bearing down on the leather top.

So if you start with the right shaped saddle for your sit bones and the bike riding style, you fine tune it with riding it. This will give you the custom fit that a plastic base saddle can't replicate.

Using too much 'conditioner' or the wrong 'conditioner' will weaken the leather fibres and the saddle life will be dramatically shortened.
Using a conditioner manufactured for upholstery or general sports equipment is not going to give you the optimal life for a tensioned vegetable tanned leather saddle. It would be fine for a Turbo saddle which has a very thin chrome tanned leather covering a plastic shell.

Brooks sell the Proofide in small volume packs as they stress that you only use a small amount, and it will go off over time. But if you apply the correct small-sized amount in line with their usage rate then it won't go rancid before it is used up.

If you want to speed up the custom forming I have read of a suggestion to lay a damp cloth over the saddle for about 30 min. Then take it for a ride using your normal riding position. After about 30 min, the combination of the dampened leather and the pressure of your sit bones will have (according to the suggestion) accelerated the breaking in period. Then let the saddle dry fully over some days. Treat it with Proofide.

I will be trying that on some saddles I have. But then I can. I also make new covers. The one I am working with is 6.4mm thick vegetable tanned and is cut to a Swallow design.