The final scene where Yuno breaks into his world is crucial for the ending, yet they saved it for the OVA. Many people I know haven't seen the OVA, and missed this final embrace.
I remember reading the final volume of the manga because the anime ending seemed inconclusive, until I realized the OVA had the final ending.
Why does the anime conclude seconds before the manga concludes?
The final volume Last Diary contains the ending where they meet each other. But the anime OVA contains the final ending and it is taken from Redial where the ending is very descriptive. This was not in Last Diary. As you mention you read the manga, so you know the difference between the ending in the anime and the manga: how Yuno Gasai from third universe meets Yukiteru god of second universe.
The OVA does not only contain the story of how Yuno meets Yukiteru but also about the other diary users and the changes in their lives. The final ending of the anime hints that they did meet each other. If you remember the ending from the anime, there is a text change of the diary from "Yuno died" to "Yuno came to see me" and the sound of something breaking and Yuno calling Yukki which leads to one conclusion that they did meet each other. You can't say it is inconclusive.
The main reason may be lack of time. So later Esuno Sakae released both Mirai Nikki: Redial and OVA where there is happy ending and other details like how the part of Murmur of first universe, which was hanging in Yuno's mobile to help her to remember about Yukki and Minene of the second universe and help them meet with each other which he was not able to do in the show.
Another reason is that, it is not necessary that the contents of the anime and the manga should be same. Manga can contain very deep story with every detail where anime covers surface. There are many other anime/manga, where the story of the manga and anime are completely different. Because release of anime is not like the release of manga.
