If Walsh finds us one player a window, who we don't know much about, and he turns out to be a good buy, he's doing his job. You can't expect more that that. So far he's achieved that with Gueye in the summer and it looks that way with Lookman too last month.
Other targets will come from well known players, some of which Koeman will have worked with before, who Koeman and Walsh both agree will improve the squad. So far Williams, Stek, Bolasie and Schniedellin.
Out of them 6 he's had an impact in, I'd say 6 good signings based on what they were brought in to do, none have been flops.
Also you can't not give credit to Walsh for bringing in a well known player. They still have to be the right fit then you still have to go and get them. If it was that simple the top clubs wouldn't have so many flops coming from well known players, often considered world class, would they?
So I think it's wrong to think Walsh was only brought in to find the next Mahrez, he is DoF, he has a say in every deal and deserves credit for every good signing well known or not.
Based on our recruitment so far, keep him all day long.