You can absolutely do that and it is fairly common. A file called LICENSE has no special legal significance. It is the responsibility of a user of the software to obtain necessary licenses, so the absence of a particular file doesn't give them any special permissions – if they don't find the license in the Readme, they cannot use the software.
Actually, many projects do not have a license in their LICENSE file, but only the license terms. There should also be some specific notice that the software can be used under those terms. Other projects have neither a license file nor a license in their Readme, but only a license identifier in package metadata. While it is usually clear what the author intended, I do not think that would be a suitable license because it's too easy to accidentally put into the metadata, e.g. as part of a template.
It may be desirable to also put a license header into all of your source files so that it is clear that they are part of the project, and that they are subject to a particular license. This can help if the source files are copied without the README, which can e.g. happen during some packaging processes or by a careless fork.
Some special file names such as LICENSE may be used by GitHub to auto-detect the repository license. If you put the license into the Readme, GH will no longer be able to recognize that. Then again, this GH license indicator is quite fragile anyway and users should not rely on it but always check the actual license.