In case of Mailtrain, Sendy, MailWizz et al. you do not send messages directly but through a paid relay, so the blacklisting is not an issue. The price is usually quite low, for example using Amazon SES costs about $100 for million messages. If the volume is low as well, then several providers have generous free tiers available (SparkPost offers 100k free messages/month), so it might not cost anything at all. SaaS providers offer convenience – you do not have to install, maintain or upgrade anything, "it just works" but in the end most of these use also a relay provider like Amazon SES to do the actual delivery