We can turn off the printing of (dur=count) by simply unsetting the count and duration properties (they are unset in the beginning, so I don't think this will break anything, but then, I'm not totally sure...)
Also added a show regtest for this case.
\tempo 8=80 c1
\tempo "Allegro" 8=80 c1
\tempo 8=80 c1
\tempo 8=80 c1
\tempo "Allegro" 8=80 c1
\tempo 8=80 c1
+
+ % Unsetting the count using only text
+ \tempo "no note (text-only)" c1
(context-spec-music
(make-sequential-music
(list
(context-spec-music
(make-sequential-music
(list
+ (make-property-unset 'tempoUnitDuration)
+ (make-property-unset 'tempoUnitCount)
(make-property-set 'tempoText text)))
'Score))
(make-property-set 'tempoText text)))
'Score))