Why use multiple full & differential backups when I can use transaction log backups?
The difference in functionality is minimal - the difference in what happens when you come to actually do a restore is tremendous.

Log backups are sequential, so in the above scenario to restore to 00:55 you would need to restore

full_backup_2018_05_09_000000.bak
diff_backup_2018_05_09_004500.bak
tran_backup_2018_05_09_005000.trn
tran_backup_2018_05_09_005500.trn


VS

full_backup_2018_05_09_000000.bak
tran_backup_2018_05_09_000500.trn
tran_backup_2018_05_09_001000.trn
tran_backup_2018_05_09_001500.trn
tran_backup_2018_05_09_002000.trn
tran_backup_2018_05_09_002500.trn
tran_backup_2018_05_09_003000.trn
tran_backup_2018_05_09_003500.trn
tran_backup_2018_05_09_004000.trn
tran_backup_2018_05_09_004500.trn
tran_backup_2018_05_09_005000.trn
tran_backup_2018_05_09_005500.trn


Utilizing DIFFs and FULLS means you don't need to replay through all those log files, which can be time consuming and potentially put a huge dent into your RTO (Recovery Time Objective)

You have to ask yourself in the event of a disaster, or any recovery scenario, how long are you willing to wait for the database to become available again - this normally dictates what methods you can then use.

Alternative answer: If you're a masochist, use just log backups.