...but can't this value be visible on the status bar instead?
No, not for the general case, because the query engine uses a streaming model, and does not know how many records in the whole dataset "are selected"--that is, how many records satisfy the criteria for selection--unless all records have in fact been fetched and tested.
there's no way to quickly see the count of results returned, is there? Can this be displayed on the status bar
Same thing: for the general case it can't be. The query engine does not know how many records satisfy the criteria expressed by the query, unless all records have in fact been fetched.
To some extent, switching fullfetch on (q.v.) addresses these concerns.
But what else could be done, to make things more intuitive?
Perhaps, for a partial fetch, the status bar could should the number of records fetched (clearly showing that it is a subset, e.g. by using familiar blue colour for text, plus possibly italics), followed by the number of selected selected within that partial set.
While, if the fetch is complete (either for a small dataset, or if fullfetch is on), the status bar could show the total number of records in black or near-black, followed by the total number of records selected in the full set.