The Monzo app’s targets functionality works differently to what you’ve described but I thought I’d mention it, in case you’re an Android user. Here’s how it works on iOS -
& it’s on the way for Android users, they’re on the roadmap here 
Perhaps some of those features could be included when the targets are reworked, after the current accounts launch.
I’d like to be able to factor in how much I want to save each month (virtual pots will also help with this) & see how much I can spend per day, in order to meet my budget 