Spot on assessment of Scotland fans / media!
I do think that there's a strong tendency (and I've been guilty of it myself with players from Rhodes, to Kris Boyd and way back to Scott Booth) of equating early success with blindly thinking/hoping a striker will be our goal scoring machine for years to come. The reality, is that despite good initial goal scoring returns, these players are usually not of a high enough standard to do it regularly, and/or don't offer enough to the overall team given the limitations of the squad as whole.
Similarly, if a striker doesn't score in their first 5-6 caps, we tend to write them off as not good enough, regardless of how they actually played. I was guilty of this with Griffiths who had some pretty mediocre performances in his first few caps, but with the confidence of the goals against England looked so much better having bedded into international football.
With McBurnie, it could be a similar situation. He's not scored for the NT yet, and looks a bit rough around the edges, but he's only 22, has good physical assets to be a number 9. In addition, he's wracked up a decent number of minutes at EPL level, before scoring a good number of goals in the Championship for Barnsley and now Swansea, so he certainly looks like a player we should persist with and give enough chances to prove if he can cut it at international level.