After discussion around #9024, I'm coming to realize that there are a lot of inconsistencies with the pandas DataFrame serialization when we have to autodetect the schema. I propose that we warn when we are given a DataFrame but can't determine the correct schema.

I realize this will be a step backwards in terms of usability. I think the following feature requests are needed to be prioritized if we proceed with this deprecation:

• BigQuery: Allow partial schema in load_table_from_dataframe #8140 Allow partial schemas, so that someone can just override certain object dtype columns, for example.
• BigQuery: get table schema if not supplied (and have pyarrow) in load_table_from_dataframe #8142 Get table schema if not supplied. This covers the case when appending rows to an existing table.
• BigQuery: load_table_from_dataframe automatically generate schema for known dtypes #9044 Generate a (partial) schema for known dtypes, and merge with the provided schema.
• BigQuery: Load to table from dataframe without index #5572 (comment) Add index(es) to serialized file if specified in job_config.schema.