It seems as though you’re in quite an unusual position OP, if you buy houses so frequently that you have the local EAs filtering houses for you, so I assume you either have a property portfolio or you buy and sell frequently.
For most people, that’s not the case. There’s a fine line between offering a figure for negotiation and offering such a low figure that the vendor refuses to countenance any other offer from you. It also depends on the market in the area and whether the vendor needs or wants to sell. The two are different. At present, in many areas it’s a buyers market, so low offers are common, but then onward purchases are probably lower too. I’d also consider the position of a prospective purchaser. The EA should advise about that.
It is a business transaction, but it differed from many business transactions, in that a house is a home where you have lived, perhaps raised a family, invested time care and attention on making it the way you want it. That, inevitably is a conflict between head and heart.
Many years ago, our house was on the market for £425K. A young couple, living with parents, offered £385K. The agent was really not happy to tell me that. It was refused. Time went by and the couple offered £395K, also refused. More time, then they offered £405K, then £415K, then £420K. We accepted then, but it pained me to do so and we only accepted because they were in a good position and there was no chain.