I do tear a new edge typically after I've washed the fabric. The yardage is generally so badly cut/folded on the bolt that I rarely get anything close to a straight cut. I figure out the low side and snip about 1/2" from the edge, typically I get about 2" off on the long side. I don't starch, but my prepared fabric is crisp and folded into fourths and ready to be cut into strips. I used to leave the corresponding raw edge ragged but over the years I've gotten fussy and cut/tear off both ends.
It can make a person angry if they let it, the terrible bad cuts we get, again it isn't all the cutter's fault though, some of it is how it is on the bolt. And don't get me started on how awful I've found store cut fat quarters... But yeah, if I have two ends both 4" off, that's 8" or an 8th of a yard of loss which is just not money nor fabric I wish to throw away but neither is it usable to me. 2.5" seems excessive, you do need about half an inch to start for a good tear, and then I cut off about 1/4" with the rotary cutter to take off the warp from the tear. I've started buying an additional half yard of extra wide backing fabric because I'm tired of not having enough after you take care of the bad cuts.
I'm big on being straight on grain because that was what I was taught in Home Ec back in the day... how to pull a strand and then cut along it. The reality is that it doesn't matter so much really, at least depending on what you are doing. I will fussy cut fabric with no regard at all to grain line. The grain can and does matter on bias edges, some people have more problems with bias than I seem to.
If you are really fussy, you should know that tearing isn't enough! With the high speed processes during the process both in the initial weaving and again in the folding and putting on the bolt, the fabric can be twisted or skewed. So your selvedges can be straight and true or the tear line, but not both. In those cases most of us just pick a good compromise, or you can tug on the fabric from the opposite diagonal/bias corners and straighten the fabric.
The big thing is when you cut your first strip from your prepared fabric is to unfold it and look at it. It should be straight with no big V at the fold line. I check my strips about every 3-5 cuts to make sure I'm still cutting straight and the fabric is still straight.
On the downside of being correct with grain is I seem to be covered in a lot more threads than people who are deliberately slightly skewed!