It's been a while since i took part in using a website-based flight booking system and this is because I stopped seeing the benefits of using them. Travel agents still exist and most of them will do almost anything it takes in order to please you and make a sale because their industry was basically decimated by the emergence of DIY'ers that were going to use Expedia, Trips.com, Agoda, and others that are all competing with one another on only one front: Price.

To me this isn't necessarily a good thing, finding the lowest price, because often, in their somewhat devious methods of trying to be the number one low cost provider, they will sell you a kind of bad bill of goods and conceal this from you until it is too late for you to do anything about it.
Case and point is them lumping in ultra-low-cost carriers into long-haul flights that have baggage fee scams and you turn up to the counter with your bags from a full-service carrier that got you this far only to discover that they are going to charge hundreds of dollars for you to check a bag. This is an obvious scam and there is no justification for it other than airlines and their partners attempting to get customers using deceit rather than genuinely better prices.
So these days I mostly use and agent for my flight bookings. I like to be able to leave the paperwork to someone else and I also enjoy being able to contact a professional if something goes wrong. I am willing to pay a premium for this.
However, I do realize that it's an evil world that we live in and I need to have some form of a starting negotiation when I talk to an agent as far as how much flights actually cost to and from that destination.
In the past I would use various websites that allowed you to search entire months to/from a location and the estimated price per direction would be highlighted by day. Almost all of the websites that i used in the past for this sort of thing have either discontinued this service or the business doesn't even exist anymore.

The only approximation of this service that I can find is google travel and it seems to have been built to be used on phones which is annoying for an old timer like me that wants to use his laptop and doesn't have good enough eyes to even attempt this on a phone. But I guess it is a start.
So if you travel like I do, with an agent but also would prefer to have a decent idea about what flights cost before you give them all the legwork to do, I think that google travel is kind of the only reliable option that we have at the moment.
I suppose I can understand why this model is not profitable because there are probably tons of people out there like me that are only looking to get information, not to actually spend any money. This might be why the major internet booking sites stopped having this option or never had it to begin with.
If you too would like to have an idea about how much a particular flight is going to be without digging too much into exact dates, I highly suggest you look at it yourself. It is free after all.