BIG Launcher Easy Phone very much fits your needs. Let me start with a quote of the app's description:
BIG Launcher makes the smartphone suitable for seniors, children, and people with eye diseases, motor problems or the legally blind. Visually impaired and technically challenged users can use the simple and easy-to-read interface with ease. There is no fear of making a mistake and losing everything with stress-free navigation. And it also features the SOS button which can save lives!
Next, let's check your listed requirements:
- No button to drop-back to the default launcher: Such a button is pretty rare. The first time you start the newly installed launcher, you will be asked whether to make it the default. Do that, and you should be fine. Additionally, again from the app's description: Full screen mode and password protection prevent the users from getting lost or from deleting something important from the phone. This creates a completely safe mobile environment.
- Large, high contrast dialer buttons: Though a dialer usually is not part of the launcher, here you go:
Screenshots from the launcher's integrated phone/dialer (source: Google Play; click images for larger variants)
- Placing and receiving calls is the most important part of the launcher.: Again, not usually part of the launcher – but part of this one. A picture says more than... well, 3 of them above.
- simple way to see and dismiss texts and other notifications: Not having used the app, I cannot tell for sure – though I'd assume that from the description. But as it's "bonus", and all other requirements are fulfilled – this should be fine.
So if you really like this one, it also has a payed version – though I find USD10 a bit heavy.
GrandPhone Senior Launcher might be an even better fit. Take the basic descriptions from above, and match them to these screens:
Dialer and Homescreen view (source: Google Play; click images for larger variants)
- less permissions required
- fresher look
- apart from that, fitting the same description
Though: it lacks the feature of protecting against accidentally hitting the "wrong button" (here: e.g. the app drawer icon).
The choice is yours. For more alternatives, be welcome to check my list of Launchers for "old folks" – a section I just set up especially for you :)