As @user25972 pointed out, it's not necessarily "baby talk" that babies prefer, but in one study (cited in the answer) it was positive emotion rather than the higher pitch of baby talk (or infant directed speech/IDS) that matters. However, there is a wealth of information on the preference of babies for baby talk over adult-directed talk (normal speech):
The most robust finding on infants' listening preferences has been widely characterized as a preference for baby talk (BT) over adult-directed speech (ADS). 1
The main point of baby talk, as offensive as it might be to adults, is that it is generally regarded as happy or positive. In fact, one study showed that the "sad" baby talk of depressed mothers may have a lasting impact on their children2:
‘Baby-talk’ is common across cultures. It underpins infant vocal preferences, and helps regulate infant engagement. Its longer-term significance is unclear. In a longitudinal study, we found indications of ‘sadness’ in postnatally depressed mothers’ baby-talk statistically mediated effects of maternal depression on offspring adolescent affective disorder. (emphasis mine)
Think about baby talk: facial expressions are usually positive and exaggerated. Pitch varies more than in ADS. It is more interesting to the baby to look at (more variation in visual cues) and it teaches something about social interaction. Vocabulary is more limited,sentence structure is shorter and more repetitive, allowing easier learning of phonemes, etc.3:
Studies now suggest that infant-directed speech (a) promotes infant attention to language, (b) fosters social interaction between infants and caregivers, and (c) informs infants about various aspects of their native language by heightening distinctions relative to the speech addressed to adults. New developments focusing on the social role of infant-directed conversational interactions highlight the importance of caregiver responsiveness to the infant. Building a communicative foundation even prior to the time language emerges is crucial for fostering language development.
Furthermore, IDS is exaggerated, meaning vowel sounds are easier to pick out:
One of the most widely cited characteristics of IDS speech is the expanded “vowel triangle". When plotted in perceptual space, vowels in IDS are farther apart than the same vowels in ADS. This larger acoustic difference has been argued to simplify infants’ task of constructing vowel categories (Kuhl et al., 1997; although cf. McMurray, Kovack-Lesh, Goodwin, & McEchron, 2013).
Social aspects of baby talk should be self-evident. When a baby says, "aahgooo" to a parent, the usual response is a delighted "Aahgooo" (IDS) back, not, "What are you trying to tell me, Jennifer? Are you hungry? What makes you say aahgooo?" The former is social interaction the baby can appreciate; the latter is confusing gobbledygook to the baby.
These attentional findings are supported by research using neurological and brain imaging methods showing that IDS results in more brain activation than ADS—for example, in infants’ left and right temporal areas (Naoi et al., 2012) and frontal lobes (Saito et al., 2007). IDS elicits increased neural activity (i.e., larger event-related potential responses) from both 6- and 13-month-olds between 600 and 800 milliseconds (N600–800), which is related to attentional processing (Zangl & Mills, 2007).
I'm limited to a phone right now, and as I am a dinosaur, constructing this answer is not easy. I will end it here, hoping that the case for baby talk has been made.
1 Infants' Listening Preferences: Baby Talk or Happy Talk?
2 Sadness in mothers’ ‘baby-talk’ predicts affective disorder in adolescent offspring
3 (Baby)Talk to Me: The Social Context of Infant-Directed Speech and Its Effects on Early Language Acquisition, Roberta Michnick Golinkoff, Dilara Deniz Can,
Melanie Soderstrom, and Kathy Hirsh-Pasek, School of Education, University of Delaware; Institute for Learning and Brain Sciences, University of Washington; Department of Psychology, University of Manitoba; and Department of Psychology, Temple University, PDF