Well, alrighty then. If you are correct, in 4 years you can throw it in my face and I will eat crow. TL;dr version follows.
FWIW, I see each sport as a separate entity with basketball having its ultimate prize as FF/NC from March Madness. I see baseball with ultimate prize being the CWS/NC.
Barnes followed the aftermath that extended from Pearl to Tyndall, which included the NCAA breathing down their necks. Voltello followed the awful Raleigh era and the surprisingly unsuccessful Serano tenure.
Both had to be rebuilt from the ashes with cast offs and wannabes. Barnes took what he could get and developed them and the team from unusual parts that traditional programs rarely use. See Grant and Admiral as examples. Haters said - "see, he can't recruit at at a high level at UT." They are silent about that today. Voltello took a type of player that small ball Serrano recruited, who is an excellent college coach, and rebuilt the roster more appropriately to compete well against the best in the SEC, which is the best in college baseball. He developed and blended in the Serrano guys who stayed and used them where they could be used - successfully - just like Barnes. Nobody says UT cannot recruit in baseball today. They had similar money to work with as the rest of the SEC - without the tradition of the elite in the SEC. Voltello doesn't even have good facilities.
Which tells me the money involved had less to do with it in those sports. However, the money did follow the success in both sports in an effort to sustain the level they achieved and move them over the top to elite status in the future. So money appeared as success was proven.
What was once gained has been totally lost in football other than tradition. Ground zero, burned to the ground. Heup comes in to rebuild with those who stayed to fight on (hmmm, character with a bit of "KMA haters") like Barnes and Voltello. Rebuild with one of the best in the nation leading the UTAD providing full support and being that same AD's guy. Rebuild with dedicated, competent leaders in the executive offices of UT. Rebuild with a proven, up and comer HC who is highly innovative and a players coach. A guy and his staff who has beaten and been highly competitive against better competition using less talent in their backgrounds. All of the needed facilities, fan support, player support, environment along with plenty of money to get the job done while playing the tough SEC schedule to achieve top 10 status long term. That's SEC division champion level. That's when even more money follows to take the next step - which is the level basketball and baseball have just started to work to attain without having the tradition of having done so in their past.
The football brand of Tennessee does have a tradition of winning it all at times in its history. It can again, now that the ingredients for success are there. Which IMO, but not yours, can happen without something negative happening to others in the SEC. Saban is a defensive guru who is dependent on hiring OC's who can innovate. He is far closer to the end of his career than the beginning. Heup is the offensive guru who is dependent on hiring DC's who can innovate. He is far closer to the beginning of his HC career than the end. To be the best you design your program to beat the very best - Bama. Nobody else in the SEC or nation matters because if you beat Bama on a regular basis, 90+% of the time you are regularly beating everybody else like Bama is doing now. Others will rise up occasionally like Clemson, LSU, etc. - to eventually fall down. Tennessee is the one program who has consistently held its own against Bama during several extended periods of its history.
IMO that began again in 2021. Time will tell. Go Vols!