It depends on question being asked.
For example:
- What to look for in a new squash racket
The question reads,
Yesterday I broke my squash racket with a particularly ill-placed split second reaction near the wall. So now I need a new racket. What should I pay attention to when buying one?
When this racket was broken is not of importance to the question so use of yesterday is OK and removing it with explicit date doesn't improve the post.
- What is the name of Pogba's body swerve played on Mustafi?
The question reads (before approval of suggested edit),
Yesterday on 7 July 2016 during ...
Mention of yesterday along with explicit date is not needed so can be removed.
- Why did a swimmer wear a swim cap with someone else's name?
The question reads (before approval of suggested edit),
Yesterday, in the 200m freestyle qualifying heat, Nimrod Shapira Bar-On (from Israel) wore a swim cap with another person's name.
Removal of yesterday with exact date of qualifying improves this post (IMO).
Other examples of suggested edit where removal of yesterday with exact date of event helps the case and got approved: 14848, 14847, 14846, 14853 and 14809
There are cases where removal of these terms doesn't improve the post like: 14840, 14837 and 14851
the post has timestamp clearly showing when it was posted - and from that the reader is able to infer what is meant by yesterday (and other similar words).
Yes, the post has timestamp but the exact date explicitly mentioned in the question body makes it easier to read and search for that event using that date (IMO). It definitely saves few seconds as we don't have to look down at the timestamp.
In conclusion,
Removal of these terms (today, yesterday, tomorrow, recently, etc.) doesn't improve the post in all cases. So, we should let a reviewer decide in case of suggested edit OR editing or suggesting edit if we think that the post will be improved.
There will be cases where approved review might get rolledback by OP or another user and these cases should be dealt in case by case basis.