While the standard might effectively call for immutable logs¹, he needs to read between the lines one step further: those logs do not need to be on the same machine. You could stream logs to another system that stores them immutably from the PoV of anyone except those with root or physical access to it. You still have a problem if an attacker gets access to both the source system(s) and the log sinks², there might be a latency issue meaning you could easily lose the last few log entries in the case of a complete disaster, and you have an extra moving part in your infrastructure to monitor, but it satisfies the requirement where immutable filesystem flags can not.
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[0] Yes, you'll know something happened, and you might guess it was malicious and not random corruption, but enough tracks might be covered to stop you working out the initial who & how.
[1] and some standars explicitly call for them
[2] Careful granular access management should largely mitigate that risk. That could be a problem if you are a small organisation trying to protect against internal disgruntled admins³, but you could use a a 3rd party log-sink service in that case.
[3] This may seem overly paranoid, but if it is required for the standard your target audience wants you to have a certificate for…, and TBH it isn't that paranoid.
Many of the arguments against just seem to come down to "I want to be a jerk".