Several blockchain consensus protocols proposed to use of Directed Acyclic Graphs (DAGs) to solve the limited processing throughput of traditional single-chain Proof-of-Work (PoW) blockchains. Many such protocols utilize a random transaction selection (RTS) strategy (e.g., PHANTOM, GHOSTDAG, SPECTRE, Inclusive, and Prism) to avoid transaction duplicates across parallel blocks in DAG and thus maximize the network throughput. However, previous research has not rigorously examined incentive-oriented greedy behaviors when transaction selection deviates from the protocol. In this work, we first perform a generic game-theoretic analysis abstracting several DAG-based blockchain protocols that use the RTS strategy, and we prove that such a strategy does not constitute a Nash equilibrium, which is contradictory to the proof in the Inclusive paper. Next, we develop a blockchain simulator that extends existing open-source tools to support multiple chains and explore incentive-based deviations from the protocol. We perform simulations with ten miners to confirm our conclusion from the game-theoretic analysis. The simulations confirm that greedy actors who do not follow the RTS strategy can profit more than honest miners and harm the processing throughput of the protocol because duplicate transactions are included in more than one block of different chains. We show that this effect is indirectly proportional to the network propagation delay. Finally, we show that greedy miners are incentivized to form a shared mining pool to increase their profits. This undermines the decentralization and degrades the design of the protocols in question. To further support our claims, we execute more complex experiments on a realistic Bitcoin-like network with more than 7000 nodes.