In short, I think it would be fun, interesting, and balanced to allow people to use the 1h modes of 2h weapons with the malus (e.g. morningstar, longsword, etc.) and the unidirectional hoplite mode for certain polearms (e.g. war spear, shortened spear, battle fork) without the use of a shield.
The restriction to such use only with a shield feels like an arbitrary and artificial barrier that limits player choice.
Especially for polearms, I think this change will deepen gameplay. Although Chivalry is (in my opinion) a vastly inferior game to Warband, one thing that I found admirably done in it were some of the polearm stab animations where you would hold the weapon with two hands, thrust, and release one hand so you could get the breadth of your shoulders into it and increase the length of your attack. This also reflects actual use as grip switching and such one handed, lengthening stabs are attested to in numerous historical sources (historicity is not a concern of mine, though it is, apparently, to developers). Because hoplite mode only has one attack and mode switching interrupts blocking and attacking, such a change would increase polearm versatility without strengthening polearms absolutely, that is, it is not as if you are simply giving polearms a longer stab but only the option to do so with serious drawbacks.
The change for 2h weapons in 1h mode is mostly in the name of variety. There is a serious dearth of slow, long 1h (the ACS at 95 speed and 105 length being the longest and one of the slowest, only the military hammer is slower) and it's just damn fun to use a goedendag or morningstar in 1h mode despite how weak they are. Adjusting for the malus and being successful is extremely gratifying and should not be restricted to shielders.
And just to reiterate, it really doesn't make any kind of sense for one to be able to wield a morningstar or spear in one hand while holding a shield with the other, but suddenly become unable to without the shield.