Both iTunes 12.6.x and Apple Configurator allow management remotely from a computer. As suggested in timothymh's answer, but this is the perfect use case for the Offload Unused Apps feature.
This feature is designed to automatically remove apps you're not using. It's a low risk approach because even though the apps are removed, any documents and data are still kept in case you want to re-install the apps later (assuming they're still available/compatible).
To enable this feature, go to Settings > iTunes & App Stores and then swipe up to reveal the Offload Unused Apps option at the bottom. Tap the switch to enable it.
- I'm not exactly sure how this feature works when first enabled. More specifically, I don't know if once you've enabled it, it will wait a period of time to determine what apps you don't use, or whether it will check your past app usage to determine what you haven't been using.
- If it was me, and just to be on the safe side, I would use your iPhone for a while before enabling this. Or, depending on the number of apps you have installed, spend a day or so making sure you've opened all of them up (at least the ones you want to keep) and then enable this option.