Is it reasonable to negotiate the price of a domain when purchasing from a major vendor, even if the minimum price is already specified in the parking, and I intend to make an offer significantly below that amount?
Should I bother contacting them at all?

Large domain vendors possess a vast quantity of domains with prices that were established at the time of domain parking entry. It is unlikely that any of these domains have been negotiated since their initial entry, and they may have been acquired during previous industry booms.
It is plausible that their current pricing may not align with today's market conditions.

It seems to me that the seller already indicates the minimum price for the domain, then there is no point in bargaining, since he will not lower the price below. On the other hand, if the system allows bargaining, then you can offer your price. In extreme cases, it will simply be rejected and you can buy a domain already at the price that is available if you really need it.

If we are talking about buying only one domain, and even an order of magnitude lower than the minimum allowable in the parking lot, then it's not even worth starting a correspondence. However, if you have an eye on buying several, especially if you are in the business of reselling domain names, then it is worth writing to the seller, even if it is a giant. There is another important detail - the place of purchase. Often, sites for buying / selling domains set a commission of 5%, but there are areas where the commission is 15%, so sellers overcharge. You should find out how much the marketplace charges for services.

The main principle of major domain players is straightforward - selling a single domain for 1 million dollars is preferred over selling ten domains for $100K each. Due to this, I personally do not believe it's worthwhile to contact them with an offer, but sometimes they may not specify a price and instead set a minimum offer of 1000 euros for insignificant domains, which ultimately wastes time.