My two cents.. in case it's helpful.
I've been in the business of converting visitors for decades. Conversion rate optimization (
CRO) is one of the most important processes in digital marketing. A great user experience is the key to increasing conversions/sales. Especially in this day and age where our attention spans are continually dwindling (the average attention span of a website visitor today is less than 7 seconds).
Point being.. buyer's are super fickle and there's no shortage of alternatives available to them so you should do
everything in your power to reduce the friction between them and a potential sale.
Based on my experience running a domain marketplace, I can tell you that it's very hard to keep buyers engaged. Unless they're super attached to the name, it's very easy to lose their interest. Heck, we've even had buyers who accepted offers after long negotiations and then went MIA because they had cold feet.
I may be wrong but my gut says those looking to hide the minimum are essentially trying to get buyers to pay higher prices. The problem with that thinking is (1) it'll scare away buyers who don't want to play the guessing game and (2) it'll lead to a decline in completed transactions due to buyer's remorse (i.e. did I bid too much? would the seller have accepted a lower offer? should I just buy another extension that's 100X cheaper? maybe I can get away with not paying? etc etc...). Ultimately, it will all lead to a lower sell-through rate.
On the other hand, if the reason behind wanting to hide the minimum is indeed to filter out spam/lowball offers than you can easily achieve that by simply increasing the minimum offer value (i.e. if you don't want to entertain $100 offers then don't set the minimum to $100). There's no other easy way to guarantee a spam-free experience. Just like the junk folder of our inbox, there will always be a certain level of crap that technology alone won't be able to filter. And if you try too hard, you risk losing real buyers.
Just put yourself in the buyer's shoes and play it out. Forget that you're a seller for a moment. Pretend like you're looking to purchase a new domain for your own business and play out both scenarios. Which option would you prefer as a buyer? Remember, if you want that sale then the customer is always right regardless of how inconvenient things are for you. That's business.