That's because the trigger is defined as a code reference, not as a sub name. It means you can modify e.g. a predicate, because it's defined by name, because modifiers redefine a method of the given name.

I see two ways how to wrap a trigger in a more Moosey way: either define a new trigger in the overridden attribute, or define the trigger as a sub that calls a method that you later modify (predicate overriding shown in the example, too):

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

{   package My;
    use Moose;

    has a1 => ( is        => 'rw',
                trigger   => \&a1_changed,
                predicate => 'has_attr' );

    has a2 => ( is      => 'rw',
                trigger => sub { $_[0]->a2_changed(@_[ 1 .. $#_ ]) } )
+;

    sub a1_changed {
        print ref shift,  ": a1 changed.\n";
    }

    sub a2_changed {
        print ref shift, ": a2 changed.\n";
    }

    __PACKAGE__->meta->make_immutable;
    no Moose;
}

{   package My::Child;
    use Moose;
    extends 'My';

    has '+a1' => ( trigger => \&a1_changed );

    sub a1_changed {
        print "Trigger 1 wrapped.\n";
        $_[0]->SUPER::a1_changed;
    };

    around a2_changed => sub {
        print "Trigger 2 wrapped\n";
        $_[0]->(@_[ 1 .. $#_ ]);
    };

    around has_attr => sub {
        print "Predicate wrapped\n";
    };

    __PACKAGE__->meta->make_immutable;
    no Moose;
}

my $o  = 'My'->new;
my $ch = 'My::Child'->new;

$o->a1(2);
$ch->a1(2);

say $o->has_attr;
say $ch->has_attr;

$o->a2(3);
$ch->a2(3);
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($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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