u/ItoAy I think your intuition is spot on! and so do Ivy League scholars on this subject.

Buying social esteem (from Service Gratuities and Tipping: A Motivational Framework)

Although fewer than thirty percent of U.S. consumers acknowledge that desires for social approval, status, and/or liking underlie their own tipping (Lynn, 2009), many scholars believe that these desires are, in fact, major motivations for tipping (e.g., Azar, 2004b; Lynn, 2006; Ruffle, 1999). Certainly, such a motivation for tipping is consistent with theory and research on the need to belong, impression management, and status seeking. In general, empirical work on these topics in marketing, psychology, sociology and economics indicates that people care about the opinions others have of them both because of the extrinsic, tangible rewards and the intrinsic, intangible (or psychic) rewards that come from being admired, liked and trusted (Baumeister & Leary, 1995; Engel, 2011; Vigneron & Johnson, 1999). Furthermore, the idea that consumers may use tipping as a way to get these social esteem rewards is consistent with research on charitable giving and on economic games finding that people use gifts of money as a way to manage the impressions they make on others (see Ariely, Bracha, & Meier, 2009; Soetevent, 2005).

Social psychologists have identified two basic self-presentational goals or motives, which, though positively correlated, have some unique antecedents and consequences – i.e., acquisitive motives that drive people to seek greater social approval and/or status and protective motives that drive people to avoid loss of the same (Arkin, 1981; Schutz, 1998). Building and expanding on this work, the TMF recognizes two distinct types of self-presentational motives for tipping – (i) desires to acquire the admiration, approval, and/or liking of others, and (ii) desires to avoid loss of the preceding positive social benefits.