Why is newly applied asphalt not smooth?
That is terrible and totally unacceptable. 

There are several issues: 1) insufficient asphalt to bind the aggregates, 2) no compaction, 3) improper aggregate mix, 

1) Asphalt (liquid) should be a thick soupy consistency that completely coats the aggregates throughout the top 2” minimum layer. 

2) With loose rocks laying on the top, this is an indication that it was not compacted. Rocks should not be able to be kicked off your driveway. 

3) The aggregate mix is very specific for good performance. There needs to be a certain amount of fines (sand), 1/4” minus (small crushed rocks), and 3/4” minus crushed rocks. This is important so that the rocks “bind” together when compacted. (There should NOT be any smooth edged rocks anywhere in the mix. Smooth rocks are not crushed rocks and will not bind together with other rocks.)

I’d dig up a couple of random spots and check the depth of the asphalt and the base. The minimum asphalt depth is 2” and minimum base is 4”...good practices require a minimum of 8” base. 

I’d also notify the local Building Official and the local Construction Contractor’s Board (CCB).  Get their CCB license number and file a complaint. (They can help to resolve the issue.) I’d also contact a local civil engineer to review the project. 

It’s the worst I’ve ever seen.