Jadasc covered most of the uses of the asset skills in his post, but he left one potentially important part out:
"•••• On-the-Job Training: Schooling is no substitute for
experience. A character who has been at her Profession for a
long time (and who dedicates herself to it, rather than just
coasting or dodging work), progresses efficiently within her
field. She learns not just facts, but patterns, tricks, shortcuts
and truisms that help her do her job well. In game terms,
characters at this level of Professional Training pay only
(new dots x 2) for Asset Skills, rather than (new dots x 3).
Drawback: The problem is that picking up new Skills is difficult for those who specialize. Buying the first dot of a new non-Asset
Skill costs one extra point of experience (four points, rather than
three). This increase does not affect raising the Skill further;
it just represents a steeper learning curve, because
the character has to shake herself out of her routine a
bit more than others in order to learn new talents." (p.69, H:tV)
In short, high levels of Professional Training reduce the price of both specialties and the skill itself. Assuming a starting level skill level of 2 for all three asset skills, you can make up the price of the merit levels by buying the skills up to 4. It is especially useful for longer campaigns, as the greater experience over the long run allows the savings to really shine.
In my current campaign, my two primary skills started at 3. To get both to 5 dots, I could either pay 54 XP naturally, or obtain Professional Training to 4 and pay 56 XP total. Then, I could also obtain discounted specialties and an entire third skill at the reduced rate, where the savings would increase radically. With an initial skill of zero in the third skill, I would save 15 XP total, which leaves enough saved to then treat many rolls in those skills as rote actions by obtaining the fifth level of the merit.
In summary, asset skills can be extremely useful if used with Professional Training, as XP will be conserved long-term while also radically increasing the chance of success through rote actions. However without Professional Training they have no real use.