Yes, this is a reasonable requirement and various licenses explicitly support this. In particular, it is common that some kind of attribution or extra disclaimers have to be preserved. In academia, it is common that grants must be acknowledged in any works they produce.
The Apache License 2.0 requires any NOTICE file to be preserved, and allows you to add to the NOTICE file when you modify the software. In section 4(d):
If the Work includes a "NOTICE" text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places:
- within a NOTICE text file distributed as part of the Derivative Works;
- within the Source form or documentation, if provided along with the Derivative Works;
- or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear.
The contents of the NOTICE file are for informational purposes only and do not modify the License. You may add Your own attribution notices within Derivative Works that You distribute, alongside or as an addendum to the NOTICE text from the Work, provided that such additional attribution notices cannot be construed as modifying the License.
The GPLv3 license family (incl. LGPLv3 and AGPLv3) allows you to add Additional Terms to the license. Here, 7(b) explicitly allows:
Requiring preservation of specified reasonable legal notices or author attributions in that material or in the Appropriate Legal Notices displayed by works containing it
This capability is compatible with the Apache 2 license. I.e. while you cannot directly copy Apache 2 licensed code into a GPLv3 project, you can first add an Additional Term that requires preservation of a NOTICE file and then copy the Apache 2 licensed code, along with relevant parts of the NOTICE file.
The GNU Free Documentation License (FDL v1.3) has a concept of Invariant Sections that must not be modified. Only Secondary Sections can be Invariant:
A "Secondary Section" is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document's overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.
There are additional preservation rules for document sections called History, Acknowledgements, Dedications, and a deletion rule for a section called Endorsements.
However, the FDL is primarily suitable for manuals or technical books (NOT for source code), and is highly incompatible with other licenses.