"Especially if in a particular sub you do ten method calls on your object — you've now replaced one param with ten function calls."

Not necessarily. If I know that I'm going to use the object 10 times in a specific sub, I can call get_handle() once and save the handle in my own variable throughout the sub.

sub z {
my $handle=get_handle();
$handle->method_a('parameter');
$handle->method_b('parameter');
$handle->method_c('parameter');
# Etc.
}
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Everything went worng, just as foreseen.