Google Analytics is free and capable, and for a small site that's a fine combination. People still move away, for these reasons.
- The script is heavy. Against lighter alternatives it costs noticeable load time. Check your page speed insights and it usually shows up among the largest items.
- It samples. On larger datasets Analytics computes from a portion of your data rather than all of it. That saves processing, but introduces bias into the decisions you base on it.
- The privacy question never fully went away. The Austrian, French, Italian and Dutch regulators ruled that the default implementation breached the GDPR, because personal data went to US servers. The Data Privacy Framework of July 2023 restored a basis for those transfers, but the two frameworks before it were both struck down by the Court of Justice. If you don't want that risk, pick a tool that keeps data in the EU.
- There's a learning curve. The tool is powerful, but most owners use a fraction of the reports. Then the complexity is a cost without a return.
- Ad blockers block it. Well over forty percent of internet users run one, and the Google script sits on virtually every block list. What you're left with is always a lower bound.