Are SQL Server's temporal tables here to stay?

I don't think the concern is legitimate. This feature is introduced in SQL Server 2016 and it's very clearly mentioned that it applies to SQL Server 2016 and later versions. Later version meaning for now it is at least SQL Server 2019 which has been released.

Temporal tables

Applies to: SQL Server 2016 (13.x) and later, Azure SQL Database, Azure SQL Managed Instance - Azure Synapse Analytics

SQL Server 2016 introduced support for temporal tables (also known as system-versioned temporal tables) as a database feature that brings built-in support for providing information about data stored in the table at any point in time rather than only the data that is correct at the current moment in time. Temporal is a database feature that was introduced in ANSI SQL 2011.

If at all, there is chance of removal of any feature or anything they do mention at Microsoft documentation, for instance "Database Mirroring". You can read the details about the same as below:

Note

This feature is in maintenance mode and may be removed in a future version of Microsoft SQL Server. Avoid using this feature in new development work, and plan to modify applications that currently use this feature. Use Always On availability groups instead.

I hope this addresses your concern.

Note: Given temporal tables are part of the ISO/ANSI SQL standard, and it's highly unlikely the feature will be removed from SQL Server.

Some of the managers in charge are concerned that as this is a relatively new feature of SQL server, and Microsoft may cease to support it.

One interpretation of this concern is related to literal deprecation and / or removal of the feature. The existing answer covers that very well.

Another interpretation is that, despite the feature continuing to live on, it may be "abandoned" and not improved significantly in future versions of SQL Server.

Consider columnstore indexes, introduced in SQL Server 2012. This feature had serious limitations in the initial release. But each new version of SQL Server since then has expanded the feature significantly - removing restrictions, adding new capabilities, new monitoring DMVs, etc.

On the other hand, something like SQLCLR has seen comparatively little innovation (or adoption!) since it's initial release in SQL Server 2005.

Is there a roadmap to this feature that says what Microsoft intends to do with this feature in the future?

Not explicitly, but one way to gauge whether a feature is not abandoned is by seeing if it gets development attention in subsequent releases. In the two major releases since 2016, there have been some improvements to temporal tables:

• SQL Server 2017
  • introduced the "Retention policy" option, which cleans up old rows in the history table
  • removed the restriction around ON DELETE CASCADE and ON UPDATE CASCADE referenced here
• SQL Server 2019
  • introduced the ability to use the stretch database feature with temporal history tables

It's also important to consider interoperability with new features. For instance, temporal tables are not compatible with the new node and edge tables introduced in SQL Server 2017. So that's kind of a strike against temporal tables in terms of being "abandoned."

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Are these concerns justified?

All in all, I agree that it's very unlikely this feature will be removed or deprecated. But if you're hoping to see the restrictions and limitations list shrink, it doesn't seem likely - at least, not based on the two major releases since V1 of the feature.