Whether you implement microservices or not (and you probably shouldn’t), your system is most probably composed of multiple components. The most straightforward system is probably made of a reverse proxy, an app, and a database. In this case, monitoring is not only a good idea, it’s a requirement. The higher the number of components through which a request may flow, the strongest the requirement.
However, monitoring is only the beginning of the journey. When requests start to fail en masse, you need an aggregated view across all components. It’s called tracing, and it’s one of the pillars of observability. The other two are metrics and logs.