No, the result is not “Republicans only have a shot if they don't compete with each other” (except to the extent it it is equally “Democrats only have a shot if they don't compete with each other”; it does disadvantage a party having support spread among many candidates vs concentrated on a smaller number, but there's nothing that makes that more true for one party that the other.) And no third party candidate ever had a chance before the blanket primary. (The blanket primary probably slightly improves this for the Green Party in certain Democratic-dominant districts, but only if Democratic support is highly concentated on a single candidate such as an in-party popular incumbent, but its still not much of a chance.) But, again, that's not new with the blanket primary; classic partisan primaries and FPTP voting were more than sufficient to make that generally the case just as it pretty much is everywhere in the country that uses those systems.
So the two things that make up “everything you said” are not the result of the system.
Your post agrees that both of those things do happen under the system, and yet your conclusion is that they don't. What kind of gymnastics is happening in your head?
No, the result is not “Republicans only have a shot if they don't compete with each other” (except to the extent it it is equally “Democrats only have a shot if they don't compete with each other”; it does disadvantage a party having support spread among many candidates vs concentrated on a smaller number, but there's nothing that makes that more true for one party that the other.) And no third party candidate ever had a chance before the blanket primary. (The blanket primary probably slightly improves this for the Green Party in certain Democratic-dominant districts, but only if Democratic support is highly concentated on a single candidate such as an in-party popular incumbent, but its still not much of a chance.) But, again, that's not new with the blanket primary; classic partisan primaries and FPTP voting were more than sufficient to make that generally the case just as it pretty much is everywhere in the country that uses those systems.
So the two things that make up “everything you said” are not the result of the system.