Personally I would strongly prefer that resume's I review were anonymized and all hints that might bias me were removed before any decisionmaker see's them or they are filtered. This could help more women and minorities get a foothold at that step in the process (I mean generally, not with me specifically).
However, while relatively simple censoring of resumes would remove some bias from review, such as race (can often be hinted at by the name or university attended), gender, etc, and it would prevent googling of the person's name, age is extremely hard to hide. You can see a person's job history, which is generally will tell you their age within +-5 years. One partial solution might be to only list job history for the previous 10 years and remove the year a degree was earned, but relative seniority at the beginning of that 10 year work history will still be a very effective proxy for determining age.
So, unfortunately I think we can't hide age in an effective way without removing critical information from a resume (removing everything else we can that can be removed should be removed or hidden), but I think it's interesting to speculate on why older workers will be filtered out. I suspect it is a belief (or intuition aka unconscious belief) that someone applying for junior or entry level positions when they are > 40yo is correlated with 'something being wrong', since if there is nothing wrong you would have expected them to have reached a point in their career that they no longer have to blindly submit resumes for these kinds of positions.
I wonder what would happen in a study like this if the resume's representing older hypothetical candidates included some kind of cover letter explaining the situation. For example, saying that they started out working at a bank for 15 years but they found a passion for cooking and that is why they only have 5 years of experience as a chef. My guess would be that not only would this undo the bias against them, but you would find a strong bias towards them (just a guess).