SMS delivery report on iOS

Firstly, you can't send a normal SMS using iMessage since they are completely different messaging services even if both can be sent from the iPhone Message App. iMesssage only relies on iCloud account and internet access (Wifi is sufficient) while SMS requires a SIM card that is functional and access to your carrier network (and not necessary GPRS, 3G, 4G...).

Secondly, it is not a network issue or a bug to not receive delivery report for SMS on iPhone as Apple never provided such service (as far as i know). Moreover there is no alternative app to deal with SMS and delivery report on iOS (while it is possible on Android OS). As far as I know alternative SMS apps are not allowed by Apple (only instant messaging apps are allowed, that are apps using a cellular connection i.e. 3G, 4G and so on).

SUMMARY

There is no option to enable SMS delivery report on iPhone and there is no app that can achieve this goal because it is not allowed by Apple.

Note: Back in the days when jailbreak was quite common a solution used to exist but jailbreak is not recommended and may be hard to achieve on recent OS.