You're adding a round trip to the database and the LLM and inserting a tool call in the conversation before it even starts generating any code.
And the reference Postgres MCP implementation doesn't include Postgres types or materialized views, and is one of the most widely used packages: Zed.dev's MCP server for example, is seemingly just a port of it and has the same problem.
If designed well - by suspending generation in memory and inserting a <function_result>, without restarting generation and fetching cache from disk - the round trip/tool call is better (costs the equivalent of 50 tokens for waiting + function_result tokens).
And you don't have to wonder about "if designed well": the reference implementation that's getting 20k downloads a week and getting embedded in downstream editors is is not designed well and will make the round trip every time and still not give the LLM the full information of the table.
Most MCP implementations are crappy half-assed implementations in similar fashion because everyone was rushing to post how they added <insert DB/API/Data Source> to MCP.
And if you're worried about "context fatigue" (you mean LLMs getting distracted by relevant information...), you should 100% prefer a well known schema format to N MCP prompt definitions with tool usage instructions that weren't even necessarily tuned for the LLM in question.
LLMs are much more easily derailed by the addition of extra tools and having to reason about when to call them and the results of calling them, than they are a prompt caching friendly block of tokens with easy to follow meaning.