You can get sued in offshore jurisdiction too. However it cost the plaintiff way more money to do so, and it is often so cost prohibitive that it gives you a better position to settle.
Why not everyone is using offshore jurisdiction to protect themselves: mainly cost. It is way more expensive to get an offshore structure: you get higher fee to create and maintain. You often need︀ also to hire a local nominee, rent a local office. Also as you have probably︁ noticed in this forum, getting a bank that will accept these structure is difficult and︂ the fee available have also high fee so it will create a lot of burden︃ for your daily operations. Last but not least, your cost for tax reporting will be︄ also increase tenfold.
Usually, one will have a local structure for operation, and transfer the︅ profit regularly to an offshore structure to keep it protected.