so yeah the obvious reason why the left shouldn’t justify its policies for non-leftist reasons is that short-term justifications are slippery and can twist in your hands, and you don’t want to put effort into undermining your own ideology.
for example, say you justified an extensive recycling program on environment grounds, then later it turned out that it actually had a higher environmental cost than straight landfill- wait shit this is a terrible example let me come in again.
say I strongly believe that these propositions are true:
A
A → B
A → C
A → D
…
perhaps proposition A is that everyone deserves equal opportunity in life, and from that I draw B (open borders!) and C (public healthcare!) and D (antiracism!) and all kinds of other things.
now perhaps I can’t convince someone of proposition A, or I’m too gutless to try, so instead I construct alternative justifications and try to sell those instead:
X → B
Y → C
Z → D
…
perhaps proposition X is we should strengthen the country (by boosting skilled immigration!), and Y is that we should strive for efficiency (public healthcare!), and Z is that we shouldn’t make Jesus cry so much (fight racism!).
but wait, these alternative justifications might prove much more than I intended! investing heavily in the military might also strengthen the country, and clamping down on premarital sex might also stop Jesus crying.
or the implications may not be factual: someone might decide that actually the country isn’t strengthened by increased immigration, and then we have a pickle on our hands; by ceding our true motivations we’ve compromised our entire political program.
this doesn’t mean you can’t mention when a policy has multiple benefits, and something can be win-win on more than one axis. but it’s almost impossible to be a win on every axis and anyone who says otherwise is lying, although typically to themselves.
Sometimes people may also not agree on the A→B, however. I’m not a Nationalist because I think my country is always correct, but for more Consequentialist reasons. Same thing for rejecting open borders. Antiracism seemed to be a good thing but as practically implemented by activists it’s a lot more mixed (see: Bernie got accused of being White Supremacist, numerous attempts to redefine both “Racism” and “Violence”.) My opposition to Communism is not because I’m against redistribution from an inherent perspective - I believe property is useful but not true - but based on how it turned out.