Couple of reasons,
- Time taken to load the diagram using Visio Web Access web part is very high.
- Microsoft no longer is recommend to use Visio Services with SharePoint Online.
Extracts from Visio Services in SharePoint Online roadmap as follows,
We no longer recommend using Visio Services (also called Visio Web Access) or the Visio Web Access Web Part with SharePoint Online. These features will be retired from Office 365 and SharePoint Online. We will stop Visio Services and stop supporting the Visio Web Access Web Part in September 2018.
Note In SharePoint Server, these features will be supported in accordance with the Microsoft Lifecycle Policy.
Use Visio Online from now on. Visio Online is your choice for future solutions in SharePoint Online. Visio Online is a new way to view, edit, and share Visio diagrams on the web. For more information, see View, create, and edit a diagram in Visio Online and Visio Online help.
- Edit the page you want to add the diagram.
- Insert Script Editor web part into the page
- Click on the "EDIT SNIPPET" and paste the following code
- Replace the value of the url with the "Embed URL" of the Visio Online document