It seems like I should be able to just send the 8 bytes that make up the 2 integers over and over.
For one thing, the number of bytes that make up a data type on the PC and the Arduino are not the same. An int on the PC is 4 bytes. On the Arduino, it is 2.
The Arduino has a long type that is 4 bytes, and matches an int on the PC.
But, think about the VALUE that you are wanting to send. Unless you have a "servo" that isn't really a servo, the value that you want to send is in the range of 0 to 179. That fits in a single byte. So, instead of needing to send 8 bytes, you really need to send just 2.
Is this a good approach?
Read what I wrote above, and them think about this. Serial data delivery is NOT guaranteed, Bytes can be lost, if a bit gets mangled, due to timing issues, noise (servos are electric motors, and generate noise) (noise is not necessarily something you can hear), and other reasons.
If you are sending s1, s2, s1, s2, s1, s2,..., think about that happens if you receive s1, s2, s1, s1, s2, s1,...
So, you might want to send some known value, that is not a valid servo position value (200 to 255, for instance), before or after each set of values. If the first, or third, value is not that value, the previous servo values are not valid, and you can ignore them and re-sync.