What normalization actually calculates
Peak normalization scans a file for its single loudest moment and calculates the exact multiplier needed to bring that peak up to (or down to) a target level, then applies that same multiplier uniformly across the entire file — it's a precise, calculated boost rather than a guess, and it guarantees no clipping since the loudest point is placed exactly at the target ceiling rather than over it.
This is different from compression or limiting, which change the dynamic relationship between quiet and loud parts of a file — normalization preserves the original dynamics exactly, just scaled up or down uniformly.
Why a playlist of normalized files can still sound uneven
Peak normalization matches peak levels, but two tracks can have identical peaks while sounding very differently loud overall, because perceived loudness depends heavily on average level and dynamic range, not just the single loudest instant — a heavily compressed, dense pop track and a quiet, dynamic acoustic recording can share the same peak level while one sounds dramatically louder throughout. This is exactly why loudness normalization (which targets average perceived loudness using standards like LUFS, rather than just peak level) exists as a more sophisticated alternative for playlist consistency.
When simple peak normalization is exactly what you need
For getting one file as loud as possible without clipping, or for a quick, safe boost when you're not trying to match multiple files to each other, peak normalization is simple, fast, and does exactly what it says — there's no need to reach for more complex loudness standards when the goal is that specific.
Normalizing doesn't fix an already-distorted recording
If a recording was already clipped or distorted at the source (recorded too loud to begin with), normalization can't undo that damage — it only scales the existing waveform, and a waveform that's already flattened by clipping stays flattened after normalization, just at a different overall level. Normalization is a volume tool, not a repair tool for damage that happened during recording.