Do PSE mods (or SE more generally) keep track of comments deleted for “ harassment, bigotry, or abuse”. Should they? If yes, are there consequences for repeat offenders?
There is no automatic consequence for repeated flags for rudeness or abuse. However, there are automatic flags raised when particular users accrue a number of these flags in a certain timeframe, prompting moderators to review the behaviour in question. This system is not perfect, so if you observe a pattern of rudeness and you want to make certain the moderators are aware of it, please do raise a custom flag explaining this pattern.
Users that repeatedly show such behaviour will often receive a message pointing this out to them, which can also include a temporary suspension, depending on the severity. The length of such suspensions increases with repeated infractions, see e.g. this post - the usual pattern is 7 days for the first issue, 30 days for the second, and a year for the third.