I don't think it's a problem to let your baby eat rice.
But It's better you cook your own sushi at home.
Outside, the rice may not be very clean (same hands and utensils that they used to chop up raw fish and meat).
I believe not all babies have to eat very soft rice from start. If your baby likes to pick up food and put into his own mouth, you can let him try it.
Traditionally, parents are taught to feed baby 'pureed food'.
But some parents in Western countries, actually SKIP PUREE and go straight to formed food directly. This is called BABY - LED WEANING - babies are encouraged to pick up foods with their own hands and eat. Although babies don't have teeth yet, they can use their gums and 'chew' quite well - as long as your food is soft enough (rice, soft fruits, soft meat etc). Show them how you eat and chew your food, they will imitate you and do the same.
My baby has tried eating food with her hands - I give her bits of rice (like adult rice), broccoli flower, steamed fruits, soft bread, steamed pumpkin and carrot, for her to pick up and chew. So far no problem, and she likes food this way. I started this when she was about 7 months old when she could sit up unsupported in her high chair and able to pick up things with her hands.
The plus point is feeding baby's easier (don't need to chase them with spoon), as long as you don't mind getting a bit messy (food over table and floor) but some babies prefer feeding themselves than being spoon-fed.