It appears difficult to use the Tesseract for these purposes without some extra mechanical agency to help control its power.
The fist time we see the Tesseract open a portal (at the end of Captain America: The First Avenger) it seems to be entirely random following it getting struck during the battle on the Valkyrie, whisking the Red Skull off to Vormir or wherever after he melted...
The second time we see it used to open a portal is when Loki uses it to get to Earth at the start the The Avengers. Some sort of contraption has been built at the S.H.I.E.L.D / NASA Dark Energy facility with Selvig's help in order to do this (with the possibility that he may have been subtly influenced to do this from a distance, evidenced by the post - credit tag at the end of Thor - "Well, I guess that's worth a look"). This first effort by Selvig is imperfect however and the portal collapses, something that is rectified by the end of the film due to the use of the Iridium in the second attempt, allowing the Chitauri to pass through.
The fourth time it is used (to allow Thor and Loki to return to Asgard) it is contained in some sort of contraption, one which did not appear recoverable along with the Tesseract during the short time available at the end of Thor: Ragnarok.
Finally, even when we see it used for the first time in Avengers: Infinity War, Thanos has to install it into the Infinity Gauntlet first, suggesting that even a being as powerful as he needs some sort of mechanism to use the stone.