The NSA does have an organization devoted to developing these sorts of attacks that make the NSO group look like a bunch of kindergarteners as evidenced by the Snowden leaks. The CIA also, independently of the NSA, has an organization that develops these sorts of attacks that make the NSO group also look like a bunch of kindergarteners as evidenced by the Vault 7 leaks. Almost without a doubt, the FBI, DHS, US Navy, US Army, and US Air Force all also have their own independent organizations that each make the NSO group looks like a bunch of kindergarteners given that developing a capability that makes NSO look like kindergarteners only costs on the order of ~$100M (i.e. less than a single jet fighter). There is absolutely nothing special about the NSO other than that they got caught and brought under the limelight.
The most likely reasons the FBI paid for access to Pegasus are: 1. It is another tool that frankly does not cost very much if you are the FBI. 2. The part of the FBI that bought it likely does not have authorization or possibly even knowledge of the other tools and contracted with NSO to gain those capabilities at the cost of just some money. This is like how a developer team in large stodgy old mega corporation might not be able to get IT to setup their servers so they just get a budget that they spend on AWS to do an end-run around their own IT organization.
The zero days are likely occasionally being discovered and fixed, but buying a zero-click zero day for Android/iPhone on the black market only costs on the order of $1-2M at retail. If you have your own competent team you can reasonably expect to find a zero-click zero day with only a few person-months of effort which, even at US wages, is only a few 100k per zero day. At those prices, you could keep a dozen or so stockpiled for less than the cost of starting a McDonalds franchise, so they likely did maintain a dozen or so at any one time, so if one was discovered they could just switch over to a different one and write off the old one as a cost of doing business.
They absolutely do have competition. One high profile example is Hacking Team. In terms of overall competition, I do not have any hard information, but given the size of the vulnerability markets there are probably at least a couple dozen to a few hundred organizations similar in scope to the NSO group. We do not hear about them because they mostly sell to governments.