Well, you're right that you should be consistent with the oil, as long as the operating conditions and usage is consistent.
For any engine, most any oil will technically wor (within reason), but a specific weight is going to be optimal in terms of wear protection, and parasitic drag losses which affect economy amd performance.
The more recently the engine was engineered and manufactured, the tighter the bearing and piston tolerances are likely to be, which allows for oils very the in viscosity to work which are easiest to pump and easiest to shed from reciprocating components. The downside being that they are less than optimal in extreme duty (meaning extended RPM, or very dusty/polluted) conditions. In cases like those, a thicker oil will slightly worsen mileage and performance but may prevent damage from abuse.
Without writing a book here on engine metallurgy and lubricants, you shouldn't switch oils around unless the conditions switch, because you should stick with what's ideal and any change from ideal is a compromise in some aspect of the engines performance.
But the "don't switch to synthetic, it'll be bad, n stuff" is a crock of
dook unless you're referring to some fossil of an engine with bearing tolerances over .003 and multi-piece rope seals. But even in those cases, some nice thick Mobil 1 15-50 synthetic rarely causes problems (especially with a splash of Lucas) and will all but stop friction wear on its antiquated iron piston rings and non-roller camshaft tappets altogether.
And I wouldn't worrying about flushing it if you're changing to synthetic, the oils are compatible. That is unless the old oil is really old and disgusting, in which case a cheap way to flush it is to change the oil and filter with cheap , store brand dead dinosaur oil (non-synthetic) and run it for 5-10 minutes so that it douches out all the nooks and crannies. Then swap to the good stuff.