Nothing stopping you replacing the (batt-)starter-alt wire with a direct batt-alt wire - unless it voids your F250 warranty. (Yes, jest kidding!)
And I am assuming your battery is in the engine bay - not rear or remote mounted.
But direct should be better - it will be shorter and hence less resistance. (Though the battery to starter cable should be pretty fat so it will have minimal resistance, but then there's the connectors...)
Note that modern vehicles include a fuse between the alternator and battery, but this is (supposedly) to protect the cable (or battery) if the cable shorts to ground - it won't protect the alternator.
But I prefer unfused "physical security" - ie, like the unfused battery to starter cable, and old skool unfused battery-alternator cables, they are physically protected from shorts - ie, good insulation (maybe shrouded), solid connectors and connections, and well mounted with no rubbing against other objects.
FYI - and older alternator (usually with an external body-mounted voltage regulator) should never come adrift from the battery. The battery is usually the voltage reference, and if the alternator "floats", its voltage generally rises and blows vehicles electrics. Hence a reason against a fuse.
However if all electrics are from the battery, that shouldn't be a problem. (Generally they were, with some only powering headlights direct from the alternator.)
[ Modern alternators with integral regulators have their own voltage reference and hence the battery can be disconnected, but then there is no battery to
squash damaging voltage spikes. ]
And BTW, if it is physically ok to add the new alternator-battery cable to the alternator with the existing alt-starter wire(s), why not keep the old? It can only reduce resistance, and adds a redundant path. But if it's too messy...
And BTW#2, if you have an old externally regulated alternator,
next time you have charging problems, ditch both and get an "
all in one" alternator - they are far superior (with less problems and risks). I'd suggest a
2-wire alternator aka SL type - Sense and charge Light. The S goes to the battery for an accurate battery voltage reading (no matter where the battery is), and the L is your normal chargeLight circuit. (There are also 3-wire SIL types - Sense-Ignition-chargeLight, but these have generally been replaced by the 2-wire types, except for single-wire types (D+ - the same as L).