I've worked at companies where an admin role is able to select and view another user's private data (view the system as if through another user's eyes). In today's day and age, is this good, ethical practice?
Generally yes. An admin is typically representing the data controller directly (and may even be employed by them), and access to their data is often both useful and necessary as part of the service they are providing. Data processors (third parties acting on behalf of the data controller) in that role are subject to a data processing agreement that will usually include confidentiality requirements – this is something I do quite often.
That said, there are scenarios where you may be handling "special category" data (to use GDPR terminology), such as medical records, where you may need to be stricter about access and processing, and you might want to make use of security measures such as encryption of data at rest - admins in that situation can control exactly what the database server does, but may not be able to see what the data contains (for example using the encryption mechanisms provided by CipherSweet).
In special category situations, GDPR requires that you conduct a data protection impact assessment (DPIA) and/or a privacy impact assessment (PIA) before implementing solutions, so that you you are able to justify your decisions should an information commissioner ask for it. These sound onerous, but they are actually an interesting exercise, helping you introspect about your internal practices more objectively. Take a look at the excellent open-source PIA tool published by the French information commissioner, CNIL, to help you build these.
So in short, it's generally OK, but there may be cases where you don't want to allow it, or only allow it when using additional security measures.