So why Christian symbolism (seemingly more representative of a sword) if most here say there was no purpose for it, in disagreement with me
I happens to be a Christogram - A monogram for Jesus, in this case the Chi (Normally identified today as an X) which was the guttural CH sound at the beginning of Christ and the Rho (normally identified today as a P) but was in Greek the RR sound of Christos (XRISTOS) in Greek.
We know that Constantine ascribed the victory at Milvian Bridge to the Christian God, and clearly the logo could be seen as a Christian Symbol, but it could also be seen as a Monogram for Constantine Romanum.
There was plenty of purpose for it for Constantine, firstly to ally Christians within the Empire (8%) with his cause, which gave him a wide base on which to build power. The authority of Empire, was a critical issue in the day, and there were plenty who would take it away, Maxentius being a clear supporter.
The choice of symbolism is possibly similar to Constantine conversion which I discussed earlier. Like most things with Constantine, it tends to be a little complex. The point I made earlier that the ChiRho does not appear on Constantine's Arch, constructed as it was by the Senate, and so, despite all manner of Symbolism, the Christian Symbolism is not there. Christianity was not at that stage the religion of Empire or Emperor.
One of the key reasons Constantine moved the capital to the site of old Byzantium was to get away from the insidious political backstabbing of Roman political life. The reason for branding is recognition, it is important in marketing, it is important in battle (don't want to kill the wrong people), and it is important in politics.