You can export without the default provider. In case you export something with all default provider in the unit process database, it will export the whole database because nearly everything is linked with everything and this will blow up the export.
Disadvantages for using system processes: no inventories visible, no supply chain visible, no modification for creating new processes possible, no change of input provider possible, no contribution tree of the supply chain visible, no sankey diagram of the supply chain visible, no data quality or uncertainty of the supply chain possible, not really an advantage of calculation speed anymore as it was the case in the past (the newest openLCA is pretty fast also with ecoinvent unit processes and/or libraries), much larger system process database size which makes storage/uploads/backups/copying more time consuming and comes with more storage requirements, searching something in the database or modifying something over SQL is much slower due to the large amounts of exchanges existing, and so on...
I personally would never use the system process version when there is a unit process version available for the exact same data set and the exact same impact results.