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Honestly, I'm surprised something like this isn't already an option. I'm not too sure if I can see reachability being swapped for multitasking, as said above it seems like Apple doesn't allow that type of customization. However, seeing as how single tap isn't being used... I could definitely see a new option under Accessibility that would allow a single tap on the home button to function as a press.

This would make sense as it would help those whose home button clicks no longer register, perhaps older folks who struggle to use enough force to push the home button (not sure if that's a valid issue, but whatever), and of course those who just wish to quickly tap instead of press.
 
Honestly, I'm surprised something like this isn't already an option. I'm not too sure if I can see reachability being swapped for multitasking, as said above it seems like Apple doesn't allow that type of customization. However, seeing as how single tap isn't being used... I could definitely see a new option under Accessibility that would allow a single tap on the home button to function as a press.

This would make sense as it would help those whose home button clicks no longer register, perhaps older folks who struggle to use enough force to push the home button (not sure if that's a valid issue, but whatever), and of course those who just wish to quickly tap instead of press.

Agreed, I'd love to see Apple implement something similar to what you outlined. I used my iPhone 5 for most of two years and am a power user (had 600 recharge cycles on that phone despite occasionally experimenting with Androids), and the home button sensor is starting to fade on me. I probably used the double-press to multitask feature dozens of thousands of times and it's taken its toll on the sensor. I'm going to have to replace the battery and home button sensor before I sell it.
 
Turn on AssistiveTouch under Accessibility. You can double tap on that virtual home button
 
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