They didn't feel that there was a need.

I think your assumption that:

"all the seasoned adventurers knew they will not follow Frodo to the Mount Doom"

is flawed.

This is the very reason that there were only 9 in the fellowship, to be able to slip in where an army could not.

`And I will choose you companions to go with you, as far as they will or fortune allows. The number must be few, since your hope is in speed and secrecy. Had I a host of Elves in armour of the Elder Days, it would avail little, save to arouse the power of Mordor.

_{The Fellowship of The Ring - The Ring Goes South}

To this effect, there were 3 who would be expected to know the way to Mordor.

• Gandalf - being learned, wise and well-travelled,
• Boromir - living as he does on the border of Mordor
• Aragorn - having travelled across most of Middle-Earth, including living in Gondor for some time.

If all three of those great men were no longer with the fellowship then what hope would a Hobbit have had to finish the task, alone.

We know in hindsight that this is exactly what happened, but that is beside the point.

It was only after losing Gandalf, and seeing the strain the lure of the Ring was having on the Fellowship that it become obvious to some (Frodo, Aragorn and possibly the other Hobbits), that the fellowship would need to be split. Culminating in Frodo making the decision after Boromir's attempted theft on Amon Hen.

As you stated Frodo made it clear that he did not know the way. While Elrond did not give Frodo a map, he did give him companions that knew the way, it can be assumed that these were in place of a map, and that at least one would be going all the way to Mount Doom with Frodo.

To attempt to answer the edit to the question

Assuming that Boromir and Aragorn were going to continue with their plan of only going to go to Minas Tirith and then part ways with those of the company that wish to follow Frodo to Mount Doom.

Boromir, Aragorn and Gandalf should have between them enough knowledge of the surrounding lands to get them to Gondor. That they do have enough knowledge is shown by them getting the fellowship to the lands of Gondor, past the Argonath and to Amon Hen before the fellowship split. This includes them taking diversions and discussion various other options of reaching their destination. They may in fact know more than a map could show as their information would be more up to date and contain things impossible, or considered to small and trivial to be shown on a map. Also a map cannot "think on it's feet", you have to take time out to consult a map to find the best route, in the heat of the moment Gandalf, Aragorn or Boromir may know the best route, at least in the short term to get out of danger.

Once the fellowship reaches Minas Tirith if Boromir and Aragorn decide to stay.

Frodo would still have Gandalf with him, his fall in Moria was unknown whilst they were in Rivendell, and his intentions can be assumed to be to go all the way with Frodo without any contradictory evidence.

One could also assume there would be the opportunity here to pick up a map or maps for the final part of their journey. It may even be argued that Gondor would have better maps of Mordor and the surrounding areas as they occupied it for many centuries following the Battle of Dagorlad and the Siege of Barad-Dûr.

They would not have to pick everything up in Rivendell, taking up valuable space, if they believed they had the knowledge within the party, and that they could pick it up further along on their journey.

Book II, Chapter 3: The Ring Goes South (with my emphasis):

Aragorn and Gandalf walked together or sat speaking of their road and the perils they would meet; and they pondered the storied and figured maps and books of lore that were in the house of Elrond. Sometimes Frodo was with them; but he was content to lean on their guidance, and he spent as much time as he could with Bilbo.

Frodo didn't bother with a map because he was quite content for others to look after that aspect of planning the journey.

Apparently, maps were very rare and valuable. They would not have been given away and it would have been very unusual to carry them around. They would have been kept in the equivalent of a scriptorium (library of scrolls) and brought out only rarely to be seen by normal folk.

I think that Mount Doom would have been visible from many miles away as well. So all Frodo needed to do was to head in the approximate direction until he saw the smoking mountain.

My take on the council of Elrond (at Rivendell) apparently leaving the actual route to Mt. Doom to chance:

With a planned roadmap, the others of the party susceptible to the ring could have "turned" and lay in ambush for Frodo. Even the council members were tempted by the power of the ring (although at least one was in denial, right? - which was obvious to some of the others), so as a reader, I made the assumption that the wisest choice was not to over-plan the operation.

The council's idea of proper planning was to select the correct ring-bearer, and not concern themselves too much with the trifling details of the physical accomplishment.

The ring knew the way back to Sauron. All the ring-bearer had to know was to go in the general direction. And then have the inner strength to make a left-turn at Mt.Doom instead of falling into Sauron's clutches.

Besides, a map lost or left behind would have allowed the enemy to ambush the route.

Obviously, in hindsight, the council made the optimal decision. But at the time of the decision at Rivendell, I think there are enough clues in the story to justify Elrond's seemingly incomplete directives.

I don't have any quoted passages, so not really expecting much agreement with this notion. I suppose an extensive quote from the meeting in Rivendell would do. Not long on quotations, but about this link? http://tolkiengateway.net/wiki/Council_of_Elrond

No mention of maps there, so this response does not directly address the OP question. It does remind us that it took two months to finalize the decision. If the decision was made in a short time, the omission of a map could be counted an oversight. Since it took so long, my take is that the lack of a roadmap was a deliberate omission.

It also reminds us that the "content of their character" of each member of the travelling party was the paramount criterion to the decision makers. Isn't reading someone's character considered by some to be a very adequate kind of roadmap? So, in a way, there was a map there all along!