The blockchain is big and ever-growing. If people really start transacting, like hundreds of millions a day pay their parking with Bitcoin, imagine the size of the data. Plus, Bitcoin can't handle it now with the 7 TPS limit.
Well, considering the size now with 7 TPS limit, 4K TPS (which is still lower than any of the major credit cards) will make things worse. 7 TPS is there for a reason.
According to the scalability document, VISA handles on average around 2,000 transactions per second
Burst capability is 10,000 TPS. I'm not sure how up-to-date this information is anyway.