A consequence of an unauthenticated reverse proxy is that complete set of requests that hit the proxy pass up the network transparently to the upstream server. Though this might fail to authenticate, it can be used as DoS attack on the server.
DDOS - Attacks on upstream servers
Depending on your implementation, (in our case it was) the proxy can be more efficient or take this load off your upstream server to fail the invalid requests and thus allow the upstream server to be more available to other clients. This is especially true if the reverse proxy is not the only ingress point for requests to the server in question or if there is an efficiency difference between the proxy and your upstream server. (eg nginx with lua vs tomcat)
DOS - Attack on the proxy
When authentication is done upstream, the proxy has to do MORE work (2-3 systems call atleast) to read and write data to send and recieve all the requests to/from upstream. Hopefully your authentication done at the proxy is lighter. If so, sending all this spurious data upstream, EVEN if it does not cause your upstream to fail, will cause the proxy to be much more loaded and cause a DOS on the proxy & will affect all other services exposed using the same proxy.
All this traffic which travels upstream, will also likley put a pressure on the proxy -> upstream link, especially this is not over LAN, depending on the size of the attack
Reacting to vulnerabilities
A proxy setup is much fewer number of boxes to manage, compared to say an upstream solution which runs on scores of VM's or boxes. If the core infrastructure for the solution has a vulnerability, the proxy without authentication just exposed your entire org to a zero day vulnerability, since these sort of solutions cannot be patched in a day, let alone convincing the companies to release a patch. However the proxy is entirely under the IT control and can be patched immediately to prevent any further vulnerabilities. The proxy effectively is a HUGE step up in security, if kept patched and uses authentication at the edge.
Risk of Open Proxy
A typical problem with proxies is that misconfigurations sometimes creep in, thus allowing the proxy to expose unintended upstream servers or locations. Without an authentication, this proxy thus starts acting like an open reverse proxy which is a real threat to the corporate LAN & even the general internet, since that is used by bad actors to hide their actual locations for attacks on other targets. Open proxies (wrt redirects) are considered to be universally bad.
By ensuring your reverse proxy has authentication, the risk of creating an open proxy becomes much more smaller.