But what if I want to deploy smart contracts to a EVM based blockchain which does not have any node providers like infura,alchemy etc?

How do I deploy to such a blockchain?

use web3js or web3 py libraries you can access blockchain RPC

Then why do we use private rpc of infura?

its depends on you if you not good in coding or setup OR you need quick and easy access you can use infura or similar .. and if you have your own infrastructure and have free time to learn and explore your own way you can use web3js, web3py etc to access your blockchain contracts

in short to make life easy :)

Where is the need for infrastructure if we just use webjs etherjs etc?Do we need to run a node to deploy contracts?

some people have their own chains run on some servers

its depends on you if you are learner you can use rinkeby or similar for free smart contract deployments and use web3js to communicate with it. and if you want to start your own self build network then you can start your own blockchain but its upto you and your business/work need

Nice

Thanks for helping

welcome