Prior work on language modeling showed conflicting findings about whether morphologically aligned approaches to tokenization improve performance, particularly for languages with complex morphology. To investigate this, we select a typologically diverse set of languages: Telugu (agglutinative), Hindi (primarily fusional with some agglutination), and English (fusional). We conduct a comprehensive evaluation of language models -- starting from tokenizer training and extending through the finetuning and downstream task evaluation. To account for the consistent performance differences observed across tokenizer variants, we focus on two key factors: morphological alignment and tokenization quality. To assess morphological alignment of tokenizers in Telugu, we create a dataset containing gold morpheme segmentations of 600 derivational and 7000 inflectional word forms. Our experiments reveal that better morphological alignment correlates positively -- though moderately -- with performance in syntax-based tasks such as Parts-of-Speech tagging, Named Entity Recognition and Dependency Parsing. However, we also find that the tokenizer algorithm (Byte-pair Encoding vs. Unigram) plays a more significant role in influencing downstream performance than morphological alignment alone. Naive Unigram tokenizers outperform others across most settings, though hybrid tokenizers that incorporate morphological segmentation significantly improve performance within the BPE framework. In contrast, intrinsic metrics like Corpus Token Count (CTC) and R\'enyi entropy showed no correlation with downstream performance.