Are champions without "proper" ultimates more difficult to design and balance? Champions like Jayce and Nidalee, or Rek'Sai and Corki.

There's three issues here: transform champions, low cooldown ults, and non-combat ults.
Transform champs: August "gypsylord" Browning said everything you need to know about those in his design insights for Gnar: (scroll down to "champion insights")
Low cooldown ults: I feel those are okay to balance, actually! Corki's long range poke turns on at six. He's just not a particularly windowed champion, but I feel that's okay for ADCs. Their ults tend to fill roles outside their core combat pattern (Jinx: low health execution / fight finisher. Ashe: global initiation. Lucian: single target pick / chase down etc). There are some non-ADCs with low cooldown combat ults (LeBlanc comes to mind), but generally these are okay to balance.
Non-combat ults: Oy vey, these are a pain. Champions have power curves, and 90% of our roster has this bump at level 6. Hitting level 6 first is important, seeing whether a champ is pre or post 6 is important for judging ganks and skirmishes, etc. If you have a non-combat ult, you tend to take the power of that bump and spread it out evenly amongst the rest of his abilities, which leads to a very lanebully-esque feeling (because they just get more and more non-windowed power over you, so if you fail to do something useful with your big windowed ability, you just lose).
We often reproduce the bump they'd get from an ACTIVE ult by giving them passive power in the ult slot. Rek'Sai gets her attack speed from the ult, Tahm Kench gets his health scaling, etc.

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