Riven and Jax aren't countered by Thornmail. If you are building Thormail to counter them you are falling into a trap. Tryn is only quasi-countered by Thornmail.
Riven does a lot of damage through her abilities, not her auto-attacks (she does auto-attack but typically doesn't build much/any attack speed). The Armor will reduce her damage, but if you just want Armor there are many better items - Randuin's, Frozen Heart, Sunfire Cape, Atma's ect depending on your champs needs. Also Riven can build tanky and easily add Magic Resistance to her build (Maw of Mal, Force of Nature, ect.) which will make the Thornmail deal piddly damage to her.
Jax is much the same case, except a lot his damage is Magic damage and isn't even reduced by armor. Further, although he does typically build attack speed and attack fast, thornmail is only reflect a portion of his auto-attack damage as his Ult passive adds magic damage to his attacks. Again, Jax is naturally kind of tank and can easily add Magic Resistance to his build (on top of what he gets freely from his Ult) to take minimal damage form Thornmail.
Characters that are actually countered by Thornmail, such as Fiora, AD Yi and other squishy characters that almost entirely rely on physical damage from their auto-attack to do damage, already struggle on Twisted Treeline and it only benefits champion diversity to remove it.