I don't remember noticing this anytime earlier. An asp-image control always generates this style attribute - style="border-width:0px;" - automatically.
This can be irritating when you actually want to display border around an image and are controlling it from a stylesheet, because the image won't display any border as its width is being set to 0 pixel.
Important thing is, if you are explicitly setting border-width for the image control then it's not a problem. Problem arises only when you are playing with stylesheet, which is the most common method used.
There are various workarounds to this problem, the one that I prefer is to make use of "!important" declaration in CSS (read more about "!important" here). This is done by setting border-width explicitly in CSS and telling browser to not to override it.
img { border-width:1px!important }
or
img {border:solid 1px black!important}
Few other workarounds are discussed here.