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UPDATE: According to recent changelogs, the bugs regarding Legatus Natus and PrimasGermaniae are fixed in Patch 1.4

Here the old answer with an explanation of the bug:

I just checked the event files for both events (LegatusNatus.txt and PrimasGermaniae.txt).

They behave pretty much in the same way, so I will only write it up for LegatusNatus.

From what I can gather, Mainz gets the title automatically within one month:

# Legatus Natus
country_event = {
    ...    
    trigger = {
        papacy_active = yes                      <-- Pope must exist
        tag = MAI                                <-- This only happens to Mainz
        exists = yes                             <-- Mainz must exist
        is_elector = yes                         <-- Mainz must be an elector
        government = theocratic_government       <-- Mainz has to be a theocracy
        NOT = { has_country_flag = happened_763 }<-- The event has not happened yet
    }

    mean_time_to_happen = { months = 1 }

    immediate = { set_country_flag = happened_763 }

    option = {
        name = "EVTOPTA763"
        add_country_modifier = {
            name = "legatus_natus"
            duration = -1
        }
    }
}

And this is where things go wrong. For Mainz to get the title there is no need for a good papal relation, and Mainz starts out with a low one in fact.

However, the event for losing the title is as follows:

# Position as Legatus Natus Revoked
country_event = {
    ...
    trigger = {
        has_country_modifier = legatus_natus <-- Country must be legatus natus
        OR = {                               <-- and either of the following is true
            capital_scope = { is_part_of_hre = no } <-- not part of the HRE
            NOT = { government = theocratic_government } <-- not a theocracy
            NOT = { religion = catholic } <-- not catholic
            NOT = { has_opinion ={ who = PAP value = 100 } } <-- not 100 relations with the Papal States
            exists = no <-- Country not existing
        }
    }

    mean_time_to_happen = { months = 1 }

    option = {
        name = "EVTOPTA964"
        remove_country_modifier = legatus_natus
        set_global_flag = no_legatus_natus
    }
}

So within another month after getting the title Mainz will lose it again due to the Papal States not having an opinion of 100 of Mainz.

If that's no bug, I don't know what is.

I guess Mainz should either get good relations with the Papal States from the beginning or only get the title after they hit the 100 relations threshold.

Also the info text for losing the title is highly confusing. Nowhere does it say that you have to have good relations to the Papal States.

Coalitions are an 'anti-blob' measure Paradox added to slow down expansion. Thus, members of the coalition (outside the target of the attack) are not part of the peace negotiation deals.

If in another war you could demand provinces from different countries, they probably were just allies (or cascade allies), but not there because of being in a coalition.