Pros & Cons of Self Hosting Bitcoin Node vs using a 3rd Party Service?
The truth is somewhere in the middle. Your colleague is correct to point out that there is an ongoing cost for maintaining your own full nodes. Beside the employee cost, there is also the cost for the actual server infrastructure, which may be higher than you think if you consider that you will need to maintain high availability,  redundancy, testing instances, and that you should sequester each foreign software from your own network and other nodes.
Overall, you can probably get away with having fewer infrastructure engineers than the count of supported cryptocurrencies, as maintaining a full node should not be a full-time effort. For example, the maintenance work between Bitcoin and bitcoin-derived altcoins such as Litecoin and BCH would have large overlaps. Cryptocurrencies with unrelated codebases and more strongly deviating APIs and data structures will be significantly more work. Frankly, the reference implementations of some &quot;top 20&quot; cryptocurrencies are inadequate for production use. If you deploy your nodes in the form of infrastructure as code, you have more development effort up front, but significantly less work later on.
However, the biggest cost difference is the time and effort you will need to invest to build out your own integrations with each different full node. The wallets packaged with full nodes usually do not scale to the needs of an enterprise, so you will likely need to invest in custom blockchain indexing, wallet software, address management, key management, transaction building, balance tracking, user management, etc. This is where the mentioned services can provide a lot of the heavy lifting. If you do end up developing your own integrations, I would definitely recommend having at least one engineer per supported cryptocurrency that is passionate about it specifically.
Even if you decide going with one of the mentioned service providers, I would heartily recommend that you run your own full nodes to reconcile the information the service provides with the corresponding blockchain data. This will still save you from doing your own wallet management, address management, transaction building, multisignature setup, simplify scaling, and let you focus on getting your business off the ground more quickly. You may even consider using a service provider intermittently, and then transition to self-hosting as you finish work on your own integrations.
Just to be clear: you fully entrust the future existence of your company to such a service provider. I hope that makes you at least a little bit uncomfortable and that you thoroughly take their approach to security and your counterparty-risk to them into account for your decision.
In the past few years, I have observed a few companies being extremely successful and rapidly leveling up their UX by focusing just on Bitcoin and sidestepping altcoins altogether. You may even consider a hybrid approach where you build your own Bitcoin solution and use a separate service for whatever alts you must support to limit your exposure.
Disclosure: In my previous job I was the UTXO Coin lead at BitGo.