Classic Traveller does apply stats to a great many common tasks that also use skills. These tasks are entirely concerned with killing people (and get a lot of attention in some corners). I refer to gun and melee skills. Both of these have required and advantageous stats levels based on the weapon in use. It's a very elegant mechanism. It models differing levels of natural ability. It In the CT tradition it also gives characters some choices to make. Should you take skills in a big heavy weapon that can tear through a hatch or a lighter weapon that you could actually hit with. In fact a rare character with advantageous STR and DEX and a heavy crossbow is downright scary (especially with a dose of Slow to let you reload and and fire each round).
So basically skills and stats are used in combat situations as a sort of 'opposed rolls system.' Stats modify a roll made against another person or entity that is trying to deny you success and may cause you injury. You wouldn't use advantageous dexterity mods in target practice, it applies to moving targets that are likely shooting back or hitting.
Except it's too good a mechanic not to apply to other situations. Why can't other pieces of equipment have required and advantageous stat levels? This would allow stats to modify skills rolls but be a level of detail that could be discarded if the referee or player wishes. While Strength and Dexterity are advantageous in combat other stats could modify other kinds of tasks.
TL 8 Vacc Suit
The TL 8 vacc suit is the best available to early spacefarers. Inflating it to a full atmosphere of pressure would cause ballooning and loss of mobility. At the partial pressures possible a pure oxygen mix is required and some resistance to movement is unavoidable. All this takes a toll on the wearer.
Required Endurance: 9 DM -2 to any physical tasks in the suit
Advantageous Endurance: 12 DM +1 to vacc suit rolls
Advanced Navigation UI
This navigation display can be installed on any bridge terminal. There is no middle ground: users either love or hate it. It does provide a huge amount of information but some find the number of readouts and links overwhelming.
Required Intelligence: 7 DM -1 to navigation, piloting and Ship's Boat tasks
Advantageous Intelligence 10 DM +1 to navigation, piloting and Ship's Boat tasks
Robes of Station
Required Intelligence: 10 DM -2 to any interpersonal tasks in the suit in high ranking social situations
Advantageous Intelligence: 12 DM +1 to any interpersonal tasks in the suit in high ranking social situations
Noble robes or power suits (for board meetings, not boarding actions. The suit provides a bonus in social situations but won't help anyone of low birth (snobs will spot a phony in a minute.)
Required Dexterity: 6 DM -1 to tasks involving air raft skill
Advantageous Dexterity: 9 DM +1 to tasks involving air raft skill
The Super Grav Speeder is a high performance grav vehicle with very sensitive controls. In the hands of a dextrous user it is extremely maneuverable and will outperform standard air rafts.
Required Dexterity 9 DM -2 to tasks involving Mechanic skill
Advantageous Dexterity Not applicable.
The TDX Blix is a high speed ground car with a reputation as a piece of junk. This does not refer to its handling but to the difficulty many mechanics have in repairs and maintenance.
As a final note, none of these pieces of equipment have to be standard. So this can be ignored by refs who do not want to work out modifiers for stats. It can be used to give players a choice. Do they want a standard speeder or a Super (for increased cost). The Super is faster (double speed say) but harder to handle if your pilot doesn't have a nimble hand on the controls. Why is the referee smiling like that?