Yes, the size of the metadata can become a problem over time but not because of performance but because of storage costs. Delta performance will not degrade due to the size of the metadata, but your cloud storage bill can increase.
By default Delta history is only maintained for 30 days: https://docs.databricks.com/delta/delta-utility.html#retrieve-delta-table-history
This can be changed by setting the "delta.logRetentionDuration" to a longer period.