I think this is where the confusion is coming from. You're correct that a read can simply ignore writes, even pending ones, at higher timestamps due to MVCC. This improves transaction concurrency.
However, if a read finds a provisional write (an intent) at a lower timestamp, it can't just ignore it. It needs to know whether to observe the write or not. So it looks up the write's transaction record and may have to wait. If the write transaction is not finalized then it needs to either wait on the transaction to finish or force the transaction's timestamp up above its read timestamp. This is true regardless of parallel commits or not.
What parallel commits gets us is a faster path to transaction commit, as irfansharif pointed out below. So the write can not only be committed faster with parallel commits, but it can also be resolved faster to get out of other reads' ways. In that way, it improves both the synchronous latency profile and the contention footprint of transactions, assuming no coordinator failures.