Just making a tl;dr of why I don't give support to this, keep in mind this is my opinion and feel free to disagree...
The idea is awesome, I would love to see it in many maps and think it would be very cool to play, but the thing called Hard Rock make all of this pretty pointless because of the AR10 cap imposed by the system, HR basically makes AR>=7 go up to 10 (or very close to it, in AR7 case) making the whole mapper work pointless. The mapper have all the work to time the song, select a lower AR specifically for that slow part, which probably won't be bellow 7 because of the current mapping meta, then a player do not like that change and just throw the HR mod and everything is AR10 making it somewhat similar to constant BPM speed mods in Stepmania.
HR with the current maps is just a bad designed mod, it basically throws 99% of insane maps to CS5/OD10/AR10, just because there are caps for both AR and OD without the Double Time mod (and even the DT have a cap too), which is pretty ironic because you can have negative AR with the Easy and Half-time mods. And since this mod cannot be removed or redesigned without completely destroying the current ranking/scoring system, this "different Approach Rates in a map" request would be just another bad design piled up into this.
It would be really cool to play a map built like this, like Zarerion said in his post, AR, BPM, SV and snapping distance are mainly what make the feeling of the map, the variable AR could help to build an even better feeling if well executed, but in the end it's just unfair if some people are competing by using a fixed speed (AR10 with HR) the whole map long.
The idea is awesome, I would love to see it in many maps and think it would be very cool to play, but the thing called Hard Rock make all of this pretty pointless because of the AR10 cap imposed by the system, HR basically makes AR>=7 go up to 10 (or very close to it, in AR7 case) making the whole mapper work pointless. The mapper have all the work to time the song, select a lower AR specifically for that slow part, which probably won't be bellow 7 because of the current mapping meta, then a player do not like that change and just throw the HR mod and everything is AR10 making it somewhat similar to constant BPM speed mods in Stepmania.
HR with the current maps is just a bad designed mod, it basically throws 99% of insane maps to CS5/OD10/AR10, just because there are caps for both AR and OD without the Double Time mod (and even the DT have a cap too), which is pretty ironic because you can have negative AR with the Easy and Half-time mods. And since this mod cannot be removed or redesigned without completely destroying the current ranking/scoring system, this "different Approach Rates in a map" request would be just another bad design piled up into this.
It would be really cool to play a map built like this, like Zarerion said in his post, AR, BPM, SV and snapping distance are mainly what make the feeling of the map, the variable AR could help to build an even better feeling if well executed, but in the end it's just unfair if some people are competing by using a fixed speed (AR10 with HR) the whole map long.