My experience with TP was that it was key to make contact on the phone after submitting the application. My applications were stalled, and I waited days with the same uncertainty and frustration as others, but once I had someone on the phone, they were able to sign off on the application in less than 30 seconds. This was not easy, as all the phone numbers officially provided were not operational.
The advice to contact an agent is likely pragmatic but also problematic - I doubt they do more than submit your documents and then know the right person to contact to have it processed in a timely fashion. It's essentially an application fee on a process that is supposed to be free of cost.
I don't say any of this to apologize for the process - it was broken and wrong and a callous way to treat visitors. My main complaint is that all the risk is loaded onto the visitor - many items you must pay for in advance with no guarantee of success or a fair process, or a refund if things go wrong. So all the power and responsibility to get things right is with TP, but all the stress and costs are borne by the visitor. If the application is stalled for some reason, it may just be ignored. If you don't have your TP 24hrs before departure, you don't even know whether to incur the additional expense of a PCR test.
I endured the process as a returning expat, but I don't think I would do it again. I would certainly recommend against it to any holidaymakers.