Let’s separate the residue from the starting.
Residue - 2-strokes are dirty and when shut off, mix remains in the carb throats where the gas evaporates, but leaving the oily reside behind. That, and any residue inside the head/cylinders, is what causes that ‘infamous blue puff’ of smoke at the next start up.
On my 2-S OBs with power trim, I’d trim them ‘in’ (rear of OB lower than front) when pulling up to my dock or mooring at the end of the day to hopefully eliminate or prevent such ‘pooling’. But not everyone has that luxury.
If you trailer it and put the OB ‘up’, do this as the LAST thing you do before you drive off, meaning putting away everything else you had in the boat first, giving time perhaps for less pooling or drainingninternally, I don’t know. Not sure you’d see any benefit by removing the fuel line and running her dry at the end of the day - will need others to comment on that idea for you.
Starting - Has this OB ever started easily since you have owned it? Maybe she just needs a good tune up, sync & link etc., as if bought used the previous Owner could have messed up the advance/timing/opening of the linkages etc., as well as the setting for the needle valves. Plus have you ever had the compression checked? Ever dine a ‘Dunk Decarb’ to it? Compression related issues can cause hard starting.
Proper plug choice AND plug gap is the #1 thing you can check for on hard starting OBs. And how old is your primer bulb? Is it holding pressure? Put end towards the OB higher than the other end (due to internal check valve) and pump until firm. If cold, advance throttle to start position, open choke lever & pull. Try again. If sputters or coughs, close choke 1/2 or all the way & try again. If flooded, close choke & open up the throttle.
Please tell us what happens when YOU are starting it ... as maybe we can then help you out better. I find new-to-me OBs to be like women ... you gotta try a few different things or methods to figure out ‘what she likes’ to get her to start up.
TIP - On most pull start motors, I have had the best luck ‘before starting it’ by leaving the choke closed and throttle all the way down, then pulling the pull start lightly 2 or 3 times. Then I pump bulb, choke, advance throttle, etc. ... and try to start it.
Overall, if the motor has been otherwise reliable and runs well once started, it sounds like it could benefit from having an experienced Pro tune it up.