It mainly means extra paperwork and a bit of extra cost, not a major obstacle, but it does need factoring into your planning rather than being an afterthought.
Because Tanzania is not part of the EATV bloc, any trip combining Tanzania with Kenya, Rwanda or Uganda requires two separate visa processes: the EATV (or a standalone visa) for whichever of the three-country bloc you are visiting, and a completely separate Tanzania visa, either the eVisa applied for online in advance or visa on arrival, regardless of which country you are travelling from immediately beforehand.
This also affects entry and exit logistics. Moving from, say, Kenya into Tanzania counts as leaving the EATV bloc, which is worth remembering if you were hoping to later return to Kenya, Rwanda or Uganda on that same EATV, since a single EATV does not cover re-entry after leaving the bloc. If your itinerary genuinely bounces back and forth, for instance Kenya, then Tanzania, then back to Kenya, you would need to plan for a second EATV application or accept the cost of re-entering under separate arrangements.
The good news is that a lot of common combined itineraries are naturally one-directional and avoid this problem entirely. A trip that goes Kenya safari, then EATV-covered Rwanda for gorillas, is fine on a single EATV throughout. A trip that goes Uganda, then Tanzania for Serengeti and Zanzibar, simply needs the Uganda eVisa or EATV for the Uganda leg and a completely separate Tanzania visa for that leg, applied for independently, with no re-entry conflict since you are not returning to the EATV bloc afterwards.
Plan your route direction with this in mind, apply for both visas with enough lead time, since Tanzania’s process runs on its own separate timeline from the EATV, and keep yellow fever documentation ready throughout, as it applies across every border in the region regardless of which visa scheme covers it.