What firearm, since it really boils down to the lube that is going to be used on it after cleaning.
With bolt action rifles where you will not have high round counts to really copper foul the barrel bore before they are cleaned, and since very little lube is used/such lube contains no cleaning agent properties, solvents like Hoppes work fine since they leave a protective coating behind in the bore.
In the case of AR rifle where CLP is being used as the lube and it does contain a cleaning agent, then the protective coating that Hoppes leaves behind is dissolved by CLP to leave a sticky mess instead.
Also to point out, Hoppes is fine for removing power type fouling, while when it comes to copper type fouling, take a lot a lot of scrubbing which can be bad instead.
Note on scrubbing, from the loading breach, to the muzzle with the rod and brushes. If pushing from the muzzle back, you can cause damage to the last inch of muzzle (read why the garand rifles had the last inch of bore worn out of them, since the USGI cleaned them with cleaning rod from the muzzle back down to the breach).
So if we back it up to say a bolt action rifle, yes something like Sweets copper solvent will clean the bore quicker with less scrubbing if the bore is really copper fouled, but since sweets does not leave a protective coating for short term storage, then you would do a quick patch of Hoppes cleaning solvent down the bore, followed with clean patches after you use the Sweets so there is a rust protection layer left behind.
In the case of the AR rifle, Sweets to clean the high build of of copper with min scrubbing, then you move onto the chamber with CLP and a chamber brush, and when that fouled CLP is pushed through the bore, its the light remnants of the lube agent in the CLP that becomes the short term storage agent left in the bore.
Bluntly, more rifle barrels have been destroyed by incorrectly/over scrubbing and lack of short term storage agents to prevent rust, then have been shot out in the civilian markets. And again, it the final lube that will be used after cleaning, that pretty much dictates the cleaning solvent that should be used to clean the rig.