NO, don't litter tests with loads of asserts.
Have one test that you have reached the correct page.
Other tests should navigate to the page and then perform additional actions which are tested. If navigating to the page actually fails the tests that do that in order to reach their pages or elements will fail.
Ideally whatever pre-conditions are required are set up in the test itself to avoid needing to navigate and perform other actions to set up the test. However this kind of setup ('grey box testing') is usually much harder than just navigating to the page and takes a much more mature testing model
Another example is authentication. Hundreds of tests may require authentication, but if auth fails you don't want to have hundreds of failures. This is usualky the place when grey box testing starts, for example coming up witha method to provide an dummy auth token that can be used for the test.