As a former travel agent, the following normally happens:
You buy a package holiday through a travel agent - the travel agent is just the agent selling holidays on behalf of the package holiday company (tour operator) - they (tour operator) pays the travel agent a commission for selling their holiday
If just an airline ticket most Travel agents charge a fee as airlines don’t pay commission on flights (normally a paltry £5 sector fee)
But….
Some travel agents are independent and are backed by larger consortiums - this gives them more buying power so the consortium goes to an operator (e.g. P&O cruises) & guarantees to sell x number of holidays … P&O then give that travel agent a better rate
Should you buy through a travel agent? I would say yes as you may pay slightly more than if you paid direct to an airline and hotel BUT you are getting their expertise in packaging and of anything should go wrong they will sort for you - especially if you are time poor!
Recently, I bought BA flight tickets online - I reserved them and then went to confirm them (they were really cheap!) but they wouldn’t confirm due to a computer error - 1 hr 44 mins later (on a national rate number 😞) I managed to get it sorted - I so wish I’d paid the travel agent £25 fee 😂
Imagine if you had booked your flights, hotel and car independently … you’ve caught covid so can’t travel - you have to cancel them all yourself - work out whether you can get a refund, etc whereas if you had booked through a travel agent, one call, they will sort (or as happened to my friend, the airline cancelled their return flight due to changing covid schedules so the TA got them a hotel sorted etc so they didn’t need to worry!)
If using a TA, make sure they have bonding arrangements in place (ABTA, TTA, etc) and if they are selling you a hotel and flight together, they are ATOL protected- this means if they go “under” you’ll get your money back
(Sorry for the long winded reply!)